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Chapter 9 A1 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-1)
9-1
Less
on R
eadi
ng G
uide
Exp
on
enti
al F
un
ctio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
95
Gle
ncoe
Alg
ebra
2
Lesson 9-1
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-1 i
n y
our
text
boo
k.
How
man
y ro
un
ds o
f pl
ay w
ould
be
nee
ded
for
a to
urn
amen
t w
ith
100
pla
yers
?7
Rea
d t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts a
bou
t th
e ex
pon
enti
al f
un
ctio
n
y�
10x
is t
rue
or f
alse
.
a.T
he
dom
ain
is
the
set
of a
ll p
osit
ive
real
nu
mbe
rs.
fals
e
b.
Th
e y-
inte
rcep
t is
1.
tru
e
c.T
he
fun
ctio
n i
s on
e-to
-on
e.tr
ue
d.
Th
e y-
axis
is
an a
sym
ptot
e of
th
e gr
aph
.fa
lse
e.T
he
ran
ge i
s th
e se
t of
all
rea
l n
um
bers
.fa
lse
2.D
eter
min
e w
het
her
eac
h f
un
ctio
n r
epre
sen
ts e
xpon
enti
al g
row
thor
dec
ay.
a.y
�0.
2(3)
xg
row
thb
.y�
3 ��x
dec
ayc.
y�
0.4(
1.01
)xg
row
th
3.S
upp
ly t
he
reas
on f
or e
ach
ste
p in
th
e fo
llow
ing
solu
tion
of
an e
xpon
enti
al e
quat
ion
.
92x
�1
�27
xO
rigi
nal
equ
atio
n
(32 )
2x�
1�
(33 )
xR
ewri
te e
ach
sid
e w
ith
a b
ase
of
3.32
(2x
�1)
�33
xP
ow
er o
f a
Po
wer
2(2x
�1)
�3x
Pro
per
ty o
f E
qu
alit
y fo
r E
xpo
nen
tial
Fu
nct
ion
s4x
�2
�3x
Dis
trib
uti
ve P
rop
erty
x�
2 �
0S
ub
trac
t 3x
fro
m e
ach
sid
e.x
�2
Ad
d 2
to
eac
h s
ide.
Rem
emb
er W
hat
Yo
u L
earn
ed
4.O
ne
way
to
rem
embe
r th
at p
olyn
omia
l fu
nct
ion
s an
d ex
pon
enti
al f
un
ctio
ns
are
diff
eren
tis
to
con
tras
t th
e po
lyn
omia
l fu
nct
ion
y�
x2an
d th
e ex
pon
enti
al f
un
ctio
n y
�2x
.Tel
l at
leas
t th
ree
way
s th
ey a
re d
iffe
ren
t.
Sam
ple
an
swer
:In
y�
x2 ,
the
vari
able
xis
a b
ase,
but
in y
�2x
,th
eva
riab
le x
is a
n e
xpo
nen
t.T
he
gra
ph
of
y�
x2
is s
ymm
etri
c w
ith
res
pec
tto
th
e y-
axis
,bu
t th
e g
rap
h o
f y
�2x
is n
ot.
Th
e g
rap
h o
f y
�x
2to
uch
esth
e x-
axis
at
(0,0
),bu
t th
e g
rap
h o
f y
�2x
has
th
e x-
axis
as
an a
sym
pto
te.
You
can
co
mp
ute
th
e va
lue
of
y�
x2
men
tally
fo
r x
�10
0,bu
t yo
u c
ann
ot
com
pu
te t
he
valu
e o
f y
�2x
men
tally
fo
r x
�10
0.
2 � 5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9A
ntic
ipat
ion
Gui
deE
xpo
nen
tial
an
d L
og
arit
hm
ic R
elat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
93
Gle
ncoe
Alg
ebra
2
Bef
ore
you
beg
in C
ha
pte
r 9
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
r di
sagr
ee,
wri
te N
S(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
9
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
exa
mpl
e of
wh
y yo
u d
isag
ree.
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Step
1
ST
EP
1S
TE
P 2
A,D
,or
NS
Sta
tem
ent
A o
r D
1.T
he
grap
h o
f an
y ex
pon
enti
al f
un
ctio
n i
s co
nti
nu
ous.
A2.
In t
he
expo
nen
tial
fu
nct
ion
y�
abx ,
if a
is n
egat
ive
then
yre
pres
ents
exp
onen
tial
dec
ay.
D
3.If
21x
�21
3 ,th
en x
�3.
A
4.T
he
inve
rse
of y
�b
xis
y�
��x .
D
5.3
2�
9 in
log
arit
hm
ic f
orm
is
log 2
3 �
9.D
6.If
log
3(2
x) �
log 3
(x2
�1)
,th
en 2
x�
x2
�1.
A7.
Th
e lo
gari
thm
of
a pr
odu
ct i
s th
e pr
odu
ct o
f th
e lo
gari
thm
s of
its
fac
tors
.D
8.4l
og59
is e
qual
to
log 5
94 .
A9.
Com
mon
log
arit
hm
s ar
e lo
gari
thm
s w
ith
a b
ase
of 2
,5,o
r 10
.D
10.
A n
atu
ral
loga
rith
m i
s a
loga
rith
m w
ith
bas
e e.
A11
.E
xpon
enti
al d
ecay
is
wh
en a
qu
anti
ty d
ecre
ases
by
a fi
xed
amou
nt
duri
ng
a ce
rtai
n p
erio
d of
tim
e.D
12.
Th
e pe
rcen
t of
in
crea
se i
n a
n e
xpon
enti
al g
row
th p
robl
em i
s ca
lled
th
e ra
te o
f gr
owth
.A
1 � b
Step
2
Chapter Resources
Chapter 9 A2 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-1)
9-1
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
97
Gle
ncoe
Alg
ebra
2
Lesson 9-1
Exp
on
enti
al E
qu
atio
ns
and
Ineq
ual
itie
sA
ll t
he
prop
erti
es o
f ra
tion
al e
xpon
ents
that
you
kn
ow a
lso
appl
y to
rea
l ex
pon
ents
.Rem
embe
r th
at a
m�
an�
am�
n,(
am)n
�am
n,
and
am
an�
am�
n.
Pro
per
ty o
f E
qu
alit
y fo
rIf
bis
a p
ositi
ve n
umbe
r ot
her
than
1,
Exp
on
enti
al F
un
ctio
ns
then
bx
�b
yif
and
only
if x
�y.
Pro
per
ty o
f In
equ
alit
y fo
rIf
b�
1
Exp
on
enti
al F
un
ctio
ns
then
bx
�b
yif
and
only
if x
�y
and
bx
�b
yif
and
only
if x
�y.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Exp
on
enti
al F
un
ctio
ns
Sol
ve 4
x�
1�
2x
�5 .
4x�
1�
2x�
5O
rigin
al e
quat
ion
(22 )
x�
1�
2x�
5R
ewrit
e 4
as 2
2 .
2(x
�1)
�x
�5
Pro
p.of
Ine
qual
ity fo
r E
xpon
entia
lF
unct
ions
2x�
2 �
x�
5D
istr
ibut
ive
Pro
pert
y
x�
7S
ubtr
act
xan
d ad
d 2
to e
ach
side
.
Sol
ve 5
2x�
1�
.
52x
�1
�O
rigin
al in
equa
lity
52x
�1
�5�
3R
ewrit
e as
5�
3 .
2x�
1 �
�3
Pro
p.of
Ine
qual
ity fo
r E
xpon
entia
l Fun
ctio
ns
2x�
�2
Add
1 t
o ea
ch s
ide.
x�
�1
Div
ide
each
sid
e by
2.
Th
e so
luti
on s
et i
s {x
|x�
�1}
.
1� 12
5
1� 12
5
1� 12
5
Sim
pli
fy e
ach
exp
ress
ion
.
1.(3
�2� )�
2�2.
25�
2��
125�
2�3.
(x�2� y
3�2� )�
2�
955
�2�
or
3125
�2�
x2 y
6
4.(x�
6� )(x�
5� )5.
(x�6� )�
5�6.
(2x
)(5x3
)
x�6�
��
5�x�
30�10
x4�
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Ch
eck
you
r so
luti
on.
7.32
x�
1�
3x�
23
8.23
x�
4x�
24
9.32
x�
1�
�
10.4
x�
1�
82x
�3
�11
.8x
�2
�12
.252
x�
125x
�2
6
13.4
�x�
�16
�5�
2014
.x�
3��
36���3 4�
615
.x�
2��
81� �1 8 ��
3
16.3
x�
4�
x�
117
.42x
�2
�2x
�1
x�
18.5
2x�
125x
�5
x�
15
19.1
04x
�1
�10
0x�
220
.73x
�49
x221
.82x
�5
�4x
�8
x�
�x
�o
r x
�0
x�
�3 41 �3 � 2
5 � 2
5 � 31 � 27
2 � 31 � 16
7 � 4
1 � 21 � 9
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1Ex
amp
le 2
9-1
Cha
pter
96
Gle
ncoe
Alg
ebra
2
Exp
on
enti
al F
un
ctio
ns
An
exp
onen
tial
fu
nct
ion
has
th
e fo
rm y
�ab
x ,w
her
e a
�0,
b�
0,an
d b
�1.
1.T
he f
unct
ion
is c
ontin
uous
and
one
-to-
one.
Pro
per
ties
of
an2.
The
dom
ain
is t
he s
et o
f al
l rea
l num
bers
.
Exp
on
enti
al F
un
ctio
n3.
The
x-a
xis
is t
he a
sym
ptot
e of
the
gra
ph.
4.T
he r
ange
is t
he s
et o
f al
l pos
itive
num
bers
if a
�0
and
all n
egat
ive
num
bers
if a
�0.
5.T
he g
raph
con
tain
s th
e po
int
(0,
a).
Exp
on
enti
al G
row
thIf
a�
0 an
d b
�1,
the
fun
ctio
n y
�ab
xre
pres
ents
exp
onen
tial g
row
th.
and
Dec
ayIf
a�
0 an
d 0
�b
�1,
the
fun
ctio
n y
�ab
xre
pres
ents
exp
onen
tial d
ecay
.
Sk
etch
th
e gr
aph
of
y�
0.1(
4)x .
Th
en s
tate
th
e
fun
ctio
n’s
dom
ain
an
d r
ange
.M
ake
a ta
ble
of v
alu
es.C
onn
ect
the
poin
ts t
o fo
rm a
sm
ooth
cu
rve.
Th
e do
mai
n o
f th
e fu
nct
ion
is
all
real
nu
mbe
rs,w
hil
e th
e ra
nge
is
the
set
of a
ll p
osit
ive
real
nu
mbe
rs.
Det
erm
ine
wh
eth
er e
ach
fu
nct
ion
rep
rese
nts
exp
onen
tial
g
row
th,d
eca
y,or
nei
ther
.a.
y�
0.5(
2)x
b.y
��
2.8(
2)x
c.y
�1.
1(0.
5)x
expo
nen
tial
gro
wth
,n
eith
er,s
ince
�2.
8,ex
pon
enti
al d
ecay
,sin
cesi
nce
th
e ba
se,2
,is
the
valu
e of
ais
les
s th
e ba
se,0
.5,i
s be
twee
ngr
eate
r th
an 1
than
0.
0 an
d 1
Sk
etch
th
e gr
aph
of
each
fu
nct
ion
.Th
en s
tate
th
e fu
nct
ion
’s d
omai
n a
nd
ran
ge.
1.y
�3(
2)x
2.y
��
2 ��x
3.y
�0.
25(5
)x
Do
mai
n:
all r
eal
Do
mai
n:
all r
eal
Do
mai
n:
all r
eal
nu
mb
ers;
Ran
ge:
all
nu
mb
ers;
Ran
ge:
all
nu
mb
ers;
Ran
ge:
all
po
siti
ve r
eal n
um
ber
sn
egat
ive
real
nu
mb
ers
po
sitiv
e re
al n
um
ber
sD
eter
min
ew
het
her
each
fun
ctio
nre
pre
sen
tsex
pon
enti
algr
owth
,dec
ay,o
rn
eith
er.
4.y
�0.
3(1.
2)x
gro
wth
5.y
��
5 ��x
nei
ther
6.y
�3(
10)�
xd
ecay
4 � 5
x
y
O
x
y
O
x
y
O
1 � 4
x�
10
12
3
y0.
025
0.1
0.4
1.6
6.4
x
y
O
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Stud
y G
uide
and
Inte
rven
tion
Exp
on
enti
al F
un
ctio
ns
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1
Exam
ple
2
Chapter 9 A3 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-1)
Prac
tice
Exp
on
enti
al F
un
ctio
ns
9-1
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
99
Gle
ncoe
Alg
ebra
2
Lesson 9-1
Sk
etch
th
e gr
aph
of
each
fu
nct
ion
.Th
en s
tate
th
e fu
nct
ion
’s d
omai
n a
nd
ran
ge.
1.y
�1.
5(2)
x2.
y�
4(3)
x3.
y�
3(0.
5)x
do
mai
n:
all r
eal
do
mai
n:
all r
eal
do
mai
n:
all r
eal
nu
mb
ers;
ran
ge:
all
nu
mb
ers;
ran
ge:
all
nu
mb
ers;
ran
ge:
all
po
siti
ve n
um
ber
sp
osi
tive
nu
mb
ers
po
siti
ve n
um
ber
s
Det
erm
ine
wh
eth
er e
ach
fu
nct
ion
rep
rese
nts
exp
onen
tial
gro
wth
or d
eca
y.
4.y
�5(
0.6)
xd
ecay
5.y
�0.
1(2)
xg
row
th6.
y�
5 �
4�x
dec
ay
Wri
te a
n e
xpon
enti
al f
un
ctio
n w
hos
e gr
aph
pas
ses
thro
ugh
th
e gi
ven
poi
nts
.
7.(0
,1)
and
(�1,
4)8.
(0,2
) an
d (1
,10)
9.(0
,�3)
an
d (1
,�1.
5)
y�
��x
y�
2(5)
xy
��
3(0.
5)x
10.(
0,0.
8) a
nd
(1,1
.6)
11.(
0,�
0.4)
an
d (2
,�10
)12
.(0,
)
and
(3,8
)
y�
0.8(
2)x
y�
�0.
4(5)
xy
��
(2)x
Sim
pli
fy e
ach
exp
ress
ion
.
13.(2
�2� )�
8�16
14.(
n�
3� )�75�
n15
15.y
�6�
�y5
�6�
y6�
6�
16.1
3�6�
�13
�24�
133�
6�17
.n3
n
n
3 �
�18
.125
�11�
5�
11�52
�11�
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Ch
eck
you
r so
luti
on.
19.3
3x �
5�
81x
�3
20.7
6x�
72x
�20
�5
21.3
6n�
5�
94n
�3
n�
22.9
2x�
1�
27x
�4
1423
.23n
�1
��
�nn
24
.164
n�
1�
1282
n�
1
BIO
LOG
YF
or E
xerc
ises
25
and
26,
use
th
e fo
llow
ing
info
rmat
ion
.T
he
init
ial
nu
mbe
r of
bac
teri
a in
a c
ult
ure
is
12,0
00.T
he
nu
mbe
r af
ter
3 da
ys i
s 96
,000
.
25.W
rite
an
exp
onen
tial
fu
nct
ion
to
mod
el t
he
popu
lati
on y
of b
acte
ria
afte
r x
days
.y
�12
,000
(2)x
26.H
ow m
any
bact
eria
are
th
ere
afte
r 6
days
?76
8,00
0
27.E
DU
CA
TIO
NA
col
lege
wit
h a
gra
duat
ing
clas
s of
400
0 st
ude
nts
in
th
e ye
ar 2
005
pred
icts
th
at i
t w
ill
hav
e a
grad
uat
ing
clas
s of
486
2 in
4 y
ears
.Wri
te a
n e
xpon
enti
alfu
nct
ion
to
mod
el t
he
nu
mbe
r of
stu
den
ts y
in t
he
grad
uat
ing
clas
s t
year
s af
ter
2005
.y
�40
00(1
.05)
t
11 � 21 � 6
1 � 8
1 � 2
1 � 4
x
y
Ox
y
Ox
y
O
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-1
Cha
pter
98
Gle
ncoe
Alg
ebra
2
Sk
etch
th
e gr
aph
of
each
fu
nct
ion
.Th
en s
tate
th
e fu
nct
ion
’s d
omai
n a
nd
ran
ge.
1.y
�3(
2)x
2.y
�2 �
�x
do
mai
n:
all r
eal n
um
ber
s;d
om
ain
:al
l rea
l nu
mb
ers;
ran
ge:
all p
osi
tive
nu
mb
ers
ran
ge:
all p
osi
tive
nu
mb
ers
Det
erm
ine
wh
eth
er e
ach
fu
nct
ion
rep
rese
nts
exp
onen
tial
gro
wth
or d
eca
y.
3.y
�3(
6)x
gro
wth
4.y
�2 �
�xd
ecay
5.y
�10
�x
dec
ay6.
y�
2(2.
5)x
gro
wth
Wri
te a
n e
xpon
enti
al f
un
ctio
n w
hos
e gr
aph
pas
ses
thro
ugh
th
e gi
ven
poi
nts
.
7.(0
,1)
and
(�1,
3)y
��
�x8.
(0,4
) an
d (1
,12)
y�
4(3)
x
9.(0
,3)
and
(�1,
6)y
�3 �
�x10
.(0,
5) a
nd
(1,1
5)y
�5(
3)x
11.(
0,0.
1) a
nd
(1,0
.5)
y�
0.1(
5)x
12.(
0,0.
2) a
nd
(1,1
.6)
y�
0.2(
8)x
Sim
pli
fy e
ach
exp
ress
ion
.
13. (3
�3� )�
3�27
14.(
x�2� )�
7�x�
14�
15.5
2�3�
�54
�3�
56�
3�16
.x3
x
x2�
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Ch
eck
you
r so
luti
on.
17.3
x�
9x
�2
18.2
2x�
3�
321
19.4
9x�
x�
�20
.43x
�2
�16
21.3
2x�
5�
27x
522
.27x
�32
x�
334 � 3
1 � 21 � 7
1 � 2
1 � 3
9 � 10
x
y
Ox
y
O
1 � 2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Skill
s Pr
acti
ceE
xpo
nen
tial
Fu
nct
ion
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 9 A4 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-1)
9-1
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
911
Gle
ncoe
Alg
ebra
2
Lesson 9-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fam
ilies
of
Cu
rves
Use
th
ese
grap
hs
for
the
pro
ble
ms
bel
ow.
1.U
se t
he
grap
h o
n t
he
left
to
desc
ribe
th
e re
lati
onsh
ip a
mon
g th
e cu
rves
y�
x�1 2� ,y�
x1,a
nd
y�
x2.
Fo
r n
��1 2�
and
n�
2,th
e g
rap
hs
are
refl
ecti
on
s o
f o
ne
ano
ther
in t
he
line
wit
h e
qu
atio
n y
�x1
.
2.G
raph
y�
xnfo
r n
�� 11 0�
,�1 4� ,
4,an
d 10
on
th
e gr
id w
ith
y�
x�1 2� ,y�
x1,a
nd
y�
x2.
See
stu
den
ts’g
rap
hs.
3.W
hic
h t
wo
regi
ons
in t
he
firs
t qu
adra
nt
con
tain
no
poin
ts o
f th
e gr
aph
sof
th
e fa
mil
y fo
r y
�xn
?
{(x,
y)�
x>
1 an
d 0
< y
<1}
an
d {
(x,y
)�0
< x
<1
and
y>
1}
4.O
n t
he
righ
t gr
id,g
raph
th
e m
embe
rs o
f th
e fa
mil
y y
�em
xfo
r w
hic
h
m�
1 an
d m
��
1.
See
stu
den
ts’g
rap
hs.
5.D
escr
ibe
the
rela
tion
ship
am
ong
thes
e tw
o cu
rves
an
d th
e y-
axis
.
the
gra
ph
s fo
r m
�1
and
m�
�1
are
refl
ecti
on
s in
th
e y-
axis
.
6.G
raph
y�
emx
for
m�
0,
�1 4� ,
�1 2� ,
2,an
d
4.
See
stu
den
ts’g
rap
hs.
m =
–1 – 4
m =
0
m =
1 – 4m =
1 – 2m
= 1
m =
2m
= 4
m =
– 2
m =
– 1
m =
–1 – 2
O
y
x
234
–2–3
–11
23
m =
– 4
Th
e F
amil
y y
� e
mx
n =
4
n =
10
n =
1 – 4
n =
1 –– 10
O
y
x
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
n =
1
n =
1 – 2
Th
e F
amil
y y
� x
n
n =
2
Enri
chm
ent
9-1
Cha
pter
910
Gle
ncoe
Alg
ebra
2
Wor
d Pr
oble
m P
ract
ice
Exp
on
enti
al F
un
ctio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.G
OLF
BA
LLS
A g
olf
ball
man
ufa
ctu
rer
pack
s 3
golf
bal
ls i
nto
a s
ingl
e pa
ckag
e.T
hre
e of
th
ese
pack
ages
mak
e a
gift
bo
x.T
hre
e gi
ft b
oxes
mak
e a
valu
e pa
ck.
Th
e di
spla
y sh
elf
is h
igh
en
ough
to
stac
k3
valu
e pa
cks
one
on t
op o
f th
e ot
her
.T
hre
e su
ch c
olu
mn
s of
val
ue
pack
s m
ake
up
a di
spla
y fr
ont.
Th
ree
disp
lay
fron
tsca
n b
e pa
cked
in
a s
ingl
e sh
ippi
ng
box
and
ship
ped
to v
ario
us
reta
il s
tore
s.H
ow m
any
golf
bal
ls a
re i
n a
sin
gle
ship
pin
g bo
x?72
9
2.FO
LDIN
GK
ay f
olds
a p
iece
of
pape
r in
hal
f ov
er a
nd
over
un
til
it i
s at
lea
st25
lay
ers
thic
k.H
ow m
any
tim
es d
oes
she
fold
th
e pa
per
in h
alf
and
how
man
yla
yers
are
th
ere?
5 ti
mes
,pro
du
cin
g 3
2 la
yers
3.SU
BSC
RIP
TIO
NS
Su
bscr
ipti
ons
to a
non
lin
e ar
ts a
nd
craf
ts c
lub
hav
e be
enin
crea
sin
g by
20%
eve
ry y
ear.
Th
e cl
ub
bega
n w
ith
40
mem
bers
.Mak
e a
grap
hof
th
e n
um
ber
of s
ubs
crib
ers
over
th
efi
rst
5 ye
ars
of t
he
clu
b’s
exis
ten
ce.
O
Subscribers
Year
y
x5
50
4.TE
NN
IS S
HO
EST
he
cost
of
a pa
ir o
fte
nn
is s
hoe
s in
crea
ses
abou
t 5.
1% e
very
year
.Abo
ut
how
mu
ch w
ould
a $
50 p
air
of t
enn
is s
hoe
s co
st 2
5 ye
ars
from
now
?$1
73.4
0
MO
NEY
For
Exe
rcis
es 5
–7,u
se t
he
foll
owin
g in
form
atio
n.
Sam
ope
ned
a s
avin
gs a
ccou
nt
that
acc
rues
com
pou
nd
inte
rest
at
a ra
te o
f 3%
an
nu
ally
.L
et P
be t
he
init
ial
amou
nt
Sam
dep
osit
edan
d le
t t
be t
he
nu
mbe
r of
yea
rs t
he
acco
un
th
as b
een
ope
n.
5.W
rite
an
equ
atio
n t
o fi
nd
A,t
he
amou
nt
of m
oney
in
th
e ac
cou
nt
afte
r t
year
s.A
ssu
me
that
Sam
mad
e m
ore
addi
tion
alde
posi
ts a
nd
no
wit
hdr
awal
s.A
�P
(1.0
3)t
6.If
Sam
ope
ned
th
e ac
cou
nt
wit
h $
500
and
mad
e n
o de
posi
ts o
r w
ith
draw
als,
how
mu
ch i
s in
th
e ac
cou
nt
10 y
ears
late
r?$6
71.9
6
7.W
hat
is
the
leas
t n
um
ber
of y
ears
it
wou
ld t
ake
for
such
an
acc
oun
t to
dou
ble
in v
alu
e?24
yea
rs
Chapter 9 A5 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lessons 9-1 and 9-2)
9-2
Read
ing
to L
earn
Mat
hem
atic
sL
og
arit
hm
s an
d L
og
arit
hm
ic F
un
ctio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
913
Gle
ncoe
Alg
ebra
2
Lesson 9-2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-2 i
n y
our
text
boo
k.
How
man
y ti
mes
lou
der
than
a w
his
per
is n
orm
al c
onve
rsat
ion
?10
4o
r 10
,000
tim
es
Rea
d t
he
Less
on
1.a.
Wri
te a
n e
xpon
enti
al e
quat
ion
th
at i
s eq
uiv
alen
t to
log
381
�4.
34�
81
b.
Wri
te a
log
arit
hm
ic e
quat
ion
th
at i
s eq
uiv
alen
t to
25�
�1 2��
.lo
g25
��
c.W
rite
an
exp
onen
tial
equ
atio
n t
hat
is
equ
ival
ent
to l
og4
1 �
0.40
�1
d.
Wri
te a
log
arit
hm
ic e
quat
ion
th
at i
s eq
uiv
alen
t to
10�
3�
0.00
1.lo
g10
0.00
1 �
�3
e.W
hat
is
the
inve
rse
of t
he
fun
ctio
n y
�5x
?y
�lo
g5
x
f.W
hat
is
the
inve
rse
of t
he
fun
ctio
n y
�lo
g 10
x?y
�10
x
2.M
atch
eac
h f
un
ctio
n w
ith
its
gra
ph.
a.y
�3x
IIIb
.y�
log 3
xI
c.y
��
�xII
I.II
.II
I.
3.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts a
bou
t th
e ex
pon
enti
al f
un
ctio
n
y�
log 5
xis
tru
eor
fal
se.
a.T
he
y-ax
is i
s an
asy
mpt
ote
of t
he
grap
h.
tru
eb
.T
he
dom
ain
is
the
set
of a
ll r
eal
nu
mbe
rs.
fals
ec.
Th
e gr
aph
con
tain
s th
e po
int
(5,0
).fa
lse
d.
Th
e ra
nge
is
the
set
of a
ll r
eal
nu
mbe
rs.
tru
ee.
Th
e y-
inte
rcep
t is
1.
fals
e
Rem
emb
er W
hat
Yo
u L
earn
ed4.
An
im
port
ant
skil
l n
eede
d fo
r w
orki
ng
wit
h l
ogar
ith
ms
is c
han
gin
g an
equ
atio
n b
etw
een
loga
rith
mic
and
exp
onen
tial
for
ms.
Usi
ng t
he w
ords
bas
e,ex
pone
nt,a
nd l
ogar
ithm
,des
crib
ean
eas
y w
ay t
o re
mem
ber
and
appl
y th
e pa
rt o
f th
e de
fin
itio
n o
f lo
gari
thm
th
at s
ays,
“log
bx
�y
if a
nd
only
if
by
�x.
”S
amp
le a
nsw
er:
In t
hes
e eq
uat
ion
s,b
stan
ds
for
bas
e.In
log
fo
rm,b
is t
he
sub
scri
pt,
and
in e
xpo
nen
tial
fo
rm,b
is t
he
num
ber
th
at is
rai
sed
to
a p
ower
.A lo
gar
ithm
is a
n e
xpo
nen
t,so
y,w
hic
h is
the
log
in t
he
first
eq
uat
ion
,bec
om
es t
he
exp
on
ent
in t
he
seco
nd
eq
uat
ion
.
x
y
Ox
y
O
x
y
O
1 � 3
1 � 21 � 5
1 � 5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
phin
g Ca
lcul
ator
Act
ivit
yR
egre
ssio
n E
qu
atio
n L
ab
9-1
Cha
pter
912
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A g
raph
ing
calc
ula
tor
can
be
use
d to
det
erm
ine
a re
gres
sion
equ
atio
n t
hat
best
fit
s a
set
of d
ata.
Th
is a
ctiv
ity
requ
ires
til
es l
abel
ed o
n o
ne
side
,an
d a
con
tain
er.
Col
lect
th
e D
ata
Ste
p1
Pla
ce t
he
tile
s on
th
e de
skto
p an
d co
un
t th
e to
tal
nu
mbe
r.R
ecor
dth
e to
tal
nu
mbe
r.T
hen
pla
ce t
he
tile
s in
th
e co
nta
iner
an
d ge
ntl
ysh
ake.
Ste
p2
Pou
r th
e ti
les
onto
th
e de
skto
p,re
mov
e al
l th
e ti
les
wit
h a
lab
elsh
owin
g,an
d se
t th
ese
asid
e.C
oun
t th
e re
mai
nin
g ti
les
wit
hou
t th
ela
bels
sh
owin
g an
d re
turn
th
em t
o th
e co
nta
iner
.S
tep
3R
ecor
d th
e da
ta i
n a
tabl
e li
ke t
his
on
e.
Ste
p4
Rep
eat
step
2 a
nd
3 u
nti
l th
e n
um
ber
of t
iles
wit
hou
t la
bels
is
zero
or t
he
nu
mbe
r re
mai
ns
con
stan
t.S
tep
5T
ake
the
tile
s th
at w
ere
set
asid
e in
Ste
p 2
and
pou
r th
em o
ut
ofth
e co
nta
iner
on
to t
he
desk
top.
Rem
ove
the
tile
s w
ith
out
the
labe
lsh
owin
g an
d co
un
t th
e ti
les
wit
h t
he
labe
l sh
owin
g.R
epea
t th
ispr
oces
s u
nti
l al
l th
e ti
les
hav
e be
en r
emov
ed.
Ste
p6
Rec
ord
the
data
in
ata
ble
like
th
is o
ne.
An
alyz
e th
e D
ata
1-6
.An
swer
s w
ill v
ary.
1.E
nte
r tr
ials
in
L1
and
nu
mbe
r of
til
es w
ith
out
labe
l sh
owin
g in
L2.
En
ter
tria
ls i
n L
3an
d n
um
ber
of t
iles
wit
h t
he
labe
l sh
owin
g in
L4.
2.U
se [
ST
AT
PL
OT
] to
mak
e a
scat
ter
plot
.Mak
e a
grap
h o
n p
aper
for
eac
hpl
ot.R
ecor
d th
e w
indo
w u
sed.
Des
crib
e th
e pa
tter
n o
f th
e po
ints
.
3.F
rom
th
e [C
AL
C]
men
u f
ind
the
regr
essi
on e
quat
ion
th
at b
est
fits
the
data
.Rec
ord
the
two
clos
est
equ
atio
ns,
rou
ndi
ng
valu
es t
o th
e n
eare
sth
un
dred
ths.
Lis
t an
d di
scu
ss t
he
ran
d/or
r2
valu
es.A
lso
incl
ude
th
egr
aph
s in
det
erm
inin
g th
e be
st-f
itti
ng
regr
essi
on e
quat
ion
.
4.S
ketc
h yo
ur b
est-
fit
regr
essi
on e
quat
ion
choi
ce f
or e
ach
scat
ter-
plot
on
pape
r.
5.D
escr
ibe
any
prob
lem
s w
ith
th
e da
ta o
r th
e re
gres
sion
equ
atio
ns.
6.In
sert
(0,
tota
l n
um
ber
of t
iles
) in
th
e ta
bles
an
d th
e li
sts.
Des
crib
e th
eef
fect
on
th
e gr
aph
s.W
hat
hap
pen
s w
ith
[P
wrR
eg]
and
[Exp
Reg
]w
hen
this
ord
ered
pai
r is
in
sert
ed?
Exp
lain
wh
y th
is o
ccu
rs?
ST
AT
Tria
lsN
umbe
r of
tile
s w
ithou
t lab
el s
how
ing
xy
1 2
Tria
lsN
umbe
r of
tile
s w
ith th
e la
bel s
how
ing
xy
1 2
Chapter 9 A6 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-2)
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
915
Gle
ncoe
Alg
ebra
2
Lesson 9-2
Solv
e Lo
gar
ith
mic
Eq
uat
ion
s an
d In
equ
alit
ies
Lo
gar
ith
mic
to
If
b�
1, x
�0,
and
log b
x�
y, t
hen
x�
by .
Exp
on
enti
al In
equ
alit
yIf
b�
1, x
�0,
and
log b
x�
y, t
hen
0 �
x�
by.
Pro
per
ty o
f E
qu
alit
y fo
r If
bis
a p
ositi
ve n
umbe
r ot
her
than
1,
Lo
gar
ith
mic
Fu
nct
ion
sth
en lo
g bx
�lo
g by
if an
d on
ly if
x�
y.
Pro
per
ty o
f In
equ
alit
y fo
r If
b�
1, t
hen
log b
x�
log b
yif
and
only
if x
�y,
L
og
arit
hm
ic F
un
ctio
ns
and
log b
x�
log b
yif
and
only
if x
�y.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Lo
gar
ith
ms
and
Lo
gar
ith
mic
Fu
nct
ion
s
Sol
ve l
og2
2x�
3.lo
g 22x
�3
Orig
inal
equ
atio
n
2x�
23D
efin
ition
of
loga
rithm
2x�
8S
impl
ify.
x�
4S
impl
ify.
Th
e so
luti
on i
s x
�4.
Sol
ve l
og5
(4x
�3)
�3.
log 5
(4x
�3)
�3
Orig
inal
equ
atio
n
0 �
4x�
3 �
53Lo
garit
hmic
to
expo
nent
ial i
nequ
ality
3 �
4x�
125
�3
Add
ition
Pro
pert
y of
Ine
qual
ities
�x
�32
Sim
plify
.
Th
e so
luti
on s
et i
s �x |
�x
�32
.3 � 4
3 � 4
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
1.lo
g 232
�3x
2.lo
g 32c
��
2
3.lo
g 2x
16 �
�2
4.lo
g 25�
��10
5.lo
g 4(5
x�
1) �
23
6.lo
g 8(x
�5)
�9
7.lo
g 4(3
x�
1) �
log 4
(2x
�3)
48.
log 2
(x2
�6)
�lo
g 2(2
x�
2)4
9.lo
g x�
427
�3
�1
10.l
og2
(x�
3) �
413
11.l
ogx
1000
�3
1012
.log
8(4
x�
4) �
215
13.l
og2
2x�
2x
�2
14.l
og5
x�
2x
�25
15.l
og2
(3x
�1)
�4
��
x�
516
.log
4(2
x) �
�x
�
17.l
og3
(x�
3) �
3�
3 �
x�
2418
.log
276x
�x
�3 � 2
2 � 3
1 � 41 � 2
1 � 3
2 � 3
1 � 2x � 2
1 � 8
1 � 185 � 3
Exer
cise
s
Exam
ple
1Ex
amp
le 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
Cha
pter
914
Gle
ncoe
Alg
ebra
2
Log
arit
hm
ic F
un
ctio
ns
and
Exp
ress
ion
s
Def
init
ion
of
Lo
gar
ith
m
Let
ban
d x
be p
ositi
ve n
umbe
rs,
b�
1.T
he lo
garit
hm o
f x
with
bas
e b
is d
enot
ed
wit
h B
ase
blo
g bx
and
is d
efin
ed a
s th
e ex
pone
nt y
that
mak
es t
he e
quat
ion
by
�x
true
.
Th
e in
vers
e of
th
e ex
pon
enti
al f
un
ctio
n y
�bx
is t
he
loga
rith
mic
fu
nct
ion
x�
by.
Th
is f
un
ctio
n i
s u
sual
ly w
ritt
en a
s y
�lo
g bx.
1.T
he f
unct
ion
is c
ontin
uous
and
one
-to-
one.
Pro
per
ties
of
2.T
he d
omai
n is
the
set
of
all p
ositi
ve r
eal n
umbe
rs.
Lo
gar
ith
mic
Fu
nct
ion
s3.
The
y-a
xis
is a
n as
ympt
ote
of t
he g
raph
.4.
The
ran
ge is
the
set
of
all r
eal n
umbe
rs.
5.T
he g
raph
con
tain
s th
e po
int
(1,
0).
Wri
te a
n e
xpon
enti
al e
qu
atio
n e
qu
ival
ent
to l
og3
243
�5.
35�
243
Wri
te a
log
arit
hm
ic e
qu
atio
n e
qu
ival
ent
to 6
�3
�.
log 6
��
3
Eva
luat
e lo
g 816
.
8�4 3�
�16
,so
log 8
16 �
.
Wri
te e
ach
eq
uat
ion
in
log
arit
hm
ic f
orm
.
1.27
�12
82.
3�4
�3.
��3
�
log
212
8 �
7lo
g3
��
4lo
g�1 7�
�3
Wri
te e
ach
eq
uat
ion
in
exp
onen
tial
for
m.
4.lo
g 15
225
�2
5.lo
g 3�
�3
6.lo
g 432
�
152
�22
53�
3�
4�5 2��
32
Eva
luat
e ea
ch e
xpre
ssio
n.
7.lo
g 464
38.
log 2
646
9.lo
g 100
100,
000
2.5
10.l
og5
625
411
.log
2781
12.l
og25
5
13.l
og2
�7
14.l
og10
0.00
001
�5
15.l
og4
�2.
51 � 32
1� 12
8
1 � 24 � 31 � 27
5 � 21 � 27
1� 34
31 � 81
1� 34
31 � 7
1 � 81
4 � 3
1� 21
6
1� 21
6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Stud
y G
uide
and
Inte
rven
tion
Lo
gar
ith
ms
and
Lo
gar
ith
mic
Fu
nct
ion
s
Exer
cise
s
Exam
ple
1
Exam
ple
2
Exam
ple
3
Chapter 9 A7 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-2)
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
917
Gle
ncoe
Alg
ebra
2
Lesson 9-2
Wri
te e
ach
eq
uat
ion
in
log
arit
hm
ic f
orm
.
1.53
�12
5lo
g5
125
�3
2.70
�1
log
71
�0
3.34
�81
log
381
�4
4.3�
4�
5.�
�3�
6.77
76�1 5�
�6
log
3�
�4
log
�1 4��
3lo
g77
766
�
Wri
te e
ach
eq
uat
ion
in
exp
onen
tial
for
m.
7.lo
g 621
6 �
363
�21
68.
log 2
64 �
626
�64
9.lo
g 3�
�4
3�4
�
10.l
og10
0.00
001
��
511
.log
255
�12
.log
328
�
10�
5�
0.00
001
25�1 2�
�5
32�3 5�
�8
Eva
luat
e ea
ch e
xpre
ssio
n.
13.l
og3
814
14.l
og10
0.00
01�
415
.log
2�
416
.log
�1 3�27
�3
17.l
og9
10
18.l
og8
419
.log
7�
220
.log
664
4
21.l
og3
�1
22.l
og4
�4
23.l
og9
9(n
�1)
n�
124
.2lo
g 232
32
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Ch
eck
you
r so
luti
ons.
25.l
og10
n�
�3
26.l
og4
x�
3x
�64
27.l
og4
x�
8
28.l
og�1 5�
x�
�3
125
29.l
og7
q�
00
�q
�1
30.l
og6
(2y
�8)
�2
y
14
31.l
ogy
16 �
�4
32.l
ogn
��
32
33.l
ogb
1024
�5
4
34.l
og8
(3x
�7)
�lo
g 8(7
x�
4)35
.log
7(8
x�
20)
�lo
g 7(x
�6)
36.l
og3
(x2
�2)
�lo
g 3x
x�
�2
2
37.S
OU
ND
An
equ
atio
n f
or l
oudn
ess,
in d
ecib
els,
is L
�10
log
10R
,wh
ere
Ris
th
e re
lati
vein
ten
sity
of
the
sou
nd.
Sou
nds
th
at r
each
lev
els
of 1
20 d
ecib
els
or m
ore
are
pain
ful
toh
um
ans.
Wh
at i
s th
e re
lati
ve i
nte
nsi
ty o
f 12
0 de
cibe
ls?
1012
38.I
NV
ESTI
NG
Mar
ia i
nve
sts
$100
0 in
a s
avin
gs a
ccou
nt
that
pay
s 4%
in
tere
stco
mpo
un
ded
ann
ual
ly.T
he
valu
e of
th
e ac
cou
nt
Aat
th
e en
d of
fiv
e ye
ars
can
be
dete
rmin
ed f
rom
th
e eq
uat
ion
log
A�
log[
1000
(1 �
0.04
)5].
Fin
d th
e va
lue
of A
to t
he
nea
rest
dol
lar.
$121
7
3 � 4
1 � 81 � 2
3 � 21
� 1000
1� 25
61 � 3
1 � 492 � 3
1 � 16
3 � 51 � 2
1 � 811 � 81
1 � 51 � 64
1 � 81
1 � 641 � 4
1 � 81
Prac
tice
Lo
gar
ith
ms
and
Lo
gar
ith
mic
Fu
nct
ion
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
Cha
pter
916
Gle
ncoe
Alg
ebra
2
Wri
te e
ach
eq
uat
ion
in
log
arit
hm
ic f
orm
.
1.23
�8
log
28
�3
2.32
�9
log
39
�2
3.8�
2�
log
8�
�2
4.�
�2�
log
�1 3��
2
Wri
te e
ach
eq
uat
ion
in
exp
onen
tial
for
m.
5.lo
g 324
3 �
535
�24
36.
log 4
64 �
343
�64
7.lo
g 93
�9�1 2�
�3
8.lo
g 5�
�2
5�2
�
Eva
luat
e ea
ch e
xpre
ssio
n.
9.lo
g 525
210
.log
93
11.l
og10
1000
312
.log
125
5
13.l
og4
�3
14.l
og5
�4
15.l
og8
833
16.l
og27
�
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Ch
eck
you
r so
luti
ons.
17.l
og3
x�
524
318
.log
2x
�3
8
19.l
og4
y�
00
�y
�1
20.l
og�1 4�
x�
3
21.l
og2
n�
�2
n�
22.l
ogb
3 �
9
23.l
og6
(4x
�12
) �
26
24.l
og2
(4x
�4)
�5
x�
9
25.l
og3
(x�
2) �
log 3
(3x)
126
.log
6(3
y�
5) �
log 6
(2y
�3)
y
8
1 � 21 � 4
1 � 641 � 31 � 31
� 625
1 � 64
1 � 3
1 � 2
1 � 251 � 25
1 � 2
1 � 91 � 9
1 � 31 � 64
1 � 64
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
9-2
9-2
Skill
s Pr
acti
ceL
og
arit
hm
s an
d L
og
arit
hm
ic F
un
ctio
ns
Chapter 9 A8 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-2)
9-2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
919
Gle
ncoe
Alg
ebra
2
Lesson 9-2
Mu
sica
l Rel
atio
nsh
ips
Th
e fr
equ
enci
es o
f n
otes
th
at a
re o
ne
octa
ve a
part
in
a m
usi
cal
scal
e ar
ere
late
d by
an
exp
onen
tial
equ
atio
n.F
or t
he
eigh
t C
not
es o
n a
pia
no,
the
equ
atio
n i
s C
n�
C12
n�
1 ,w
her
e C
nre
pres
ents
th
e fr
equ
ency
of
not
e C
n.
1.F
ind
the
rela
tion
ship
bet
wee
n C
1an
d C
2.C
2�
2C1
2.F
ind
the
rela
tion
ship
bet
wee
n C
1an
d C
4.C
4�
8C1
Th
e fr
equ
enci
es o
f co
nse
cuti
ve n
otes
are
rel
ated
by
a
com
mon
rat
io r
.Th
e ge
ner
al e
quat
ion
is
f n�
f 1rn
�1 .
3.If
th
e fr
equ
ency
of
mid
dle
C i
s 26
1.6
cycl
es p
er s
econ
d an
d th
e fr
equ
ency
of
the
nex
t h
igh
er C
is
523.
2 cy
cles
pe
r se
con
d,fi
nd
the
com
mon
rat
io r
.(H
int:
Th
e tw
o C
’s
are
12 n
otes
apa
rt.)
Wri
te t
he
answ
er a
s a
radi
cal
expr
essi
on.
r�
12 �2�
4.S
ubs
titu
te d
ecim
al v
alu
es f
or r
and
f 1to
fin
d a
spec
ific
eq
uat
ion
for
fn.
f n�
261.
1(1.
0594
6)n
�1
5.F
ind
the
freq
uen
cy o
f F
#ab
ove
mid
dle
C.
f 7�
261.
6(1.
0594
6)6
�36
9.95
6.F
rets
are
a s
erie
s of
rid
ges
plac
ed a
cros
s th
e fi
nge
rboa
rd o
f a
guit
ar.T
hey
are
spac
ed s
o th
at t
he
sou
nd
mad
e by
pre
ssin
g a
stri
ng
agai
nst
on
e fr
eth
as a
bou
t 1.
0595
tim
es t
he
wav
elen
gth
of
the
sou
nd
mad
e by
usi
ng
the
nex
t fr
et.T
he
gen
eral
equ
atio
n i
s w
n�
w0(
1.05
95)n
.Des
crib
e th
ear
ran
gem
ent
of t
he
fret
s on
a g
uit
ar.
Th
e fr
ets
are
spac
ed in
a
log
arit
hm
ic s
cale
.
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
9-2
Cha
pter
918
Gle
ncoe
Alg
ebra
2
Wor
d Pr
oble
m P
ract
ice
Lo
gar
ith
ms
and
Lo
gar
ith
mic
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.FI
SHT
he
popu
lati
on o
f si
lver
car
p h
asbe
en g
row
ing
in t
he
Mis
siss
ippi
Riv
er.
Abo
ut
ever
y 3
year
s,th
e po
pula
tion
dou
bles
.Wri
te l
ogar
ith
mic
exp
ress
ion
that
giv
es t
he
nu
mbe
r of
yea
rs i
t w
ill
take
for
th
e po
pula
tion
to
incr
ease
by
a fa
ctor
of
ten
.3l
og
210
2.PO
WER
SH
aley
tri
es t
o so
lve
the
equ
atio
n l
og4
2x�
32.S
he
got
the
wro
ng
answ
er.W
hat
was
her
mis
take
? W
hat
shou
ld t
he
corr
ect
answ
er b
e?
Fro
m s
tep
2 t
o s
tep
3,H
aley
div
ided
th
e eq
uat
ion
by
2in
corr
ectl
y.T
he
corr
ect
answ
er
is 5
12.
3.D
IGIT
SA
com
pute
r pr
ogra
mm
er w
ants
to w
rite
a f
orm
ula
th
at t
ells
how
man
ydi
gits
th
ere
are
in a
nu
mbe
r n
,wh
ere
nis
a p
osit
ive
inte
ger.
For
exa
mpl
e,if
n
�34
3,th
e fo
rmu
la s
hou
ld e
valu
ate
to3
and
if n
�10
,000
,th
e fo
rmu
la s
hou
ldev
alu
ate
to 5
.Su
ppos
e 8
�lo
g 10
n�
9.H
ow m
any
digi
ts d
oes
nh
ave?
9
1.lo
g 42x
�5
2.2x
�45
3.x
�25
4.x
�32
4.LO
GA
RIT
HM
SP
auli
ne
know
s th
atlo
g bx
�3
and
log b
y�
5.S
he
know
s th
atth
is i
s th
e sa
me
as k
now
ing
that
b3
�x
and
b5�
y.M
ult
iply
th
ese
two
equ
atio
ns
toge
ther
an
d re
wri
te i
t as
an
equ
atio
nin
volv
ing
loga
rith
ms.
Wh
at i
s lo
g bxy
?b
3 b5
�xy
,or
b8
�xy
;in
oth
erw
ord
s,lo
gb
xy�
8
MU
SIC
For
Exe
rcis
es 5
an
d 6
,use
th
efo
llow
ing
info
rmat
ion
.
Th
e fi
rst
not
e on
a p
ian
o ke
yboa
rdco
rres
pon
ds t
o a
pitc
h w
ith
a f
requ
ency
of
27.5
cycl
espe
rse
con
d.W
ith
ever
ysu
cces
sive
not
e yo
u g
o u
p th
e w
hit
e an
d bl
ack
keys
of
a pi
ano,
the
pitc
h m
ult
ipli
es b
y a
fact
or o
f �12
2� .T
he
form
ula
for
th
e fr
equ
ency
of
the
pitc
hso
un
ded
wh
en t
he
nth
not
e u
p th
e ke
yboa
rdis
pla
yed
is g
iven
by
n�
1 �
12 l
og2
.
5.T
he
pitc
h t
hat
orc
hes
tras
tu
ne
to i
s th
eA
abo
ve m
iddl
e C
.It
has
a f
requ
ency
of
440
cycl
es p
er s
econ
d.H
ow m
any
not
esu
p th
e pi
ano
keyb
oard
is
this
A?
49
6.A
not
her
pit
ch o
n t
he
keyb
oard
has
a
freq
uen
cy o
f 17
60 c
ycle
s pe
r se
con
d.H
ow m
any
not
es u
p th
e ke
yboa
rd w
ill
this
be
fou
nd?
73
f� 27
.5
Chapter 9 A9 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-3)
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Pro
per
ties
of
Lo
gar
ith
ms
9-3
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
921
Gle
ncoe
Alg
ebra
2
Lesson 9-3
Pro
per
ties
of
Log
arit
hm
sP
rope
rtie
s of
exp
onen
ts c
an b
e u
sed
to d
evel
op t
he
foll
owin
g pr
oper
ties
of
loga
rith
ms.
Pro
du
ct P
rop
erty
F
or a
ll po
sitiv
e nu
mbe
rs m
, n,
and
b,
whe
re b
�1,
o
f L
og
arit
hm
slo
g bm
n�
log b
m�
log b
n.
Qu
oti
ent
Pro
per
ty
For
all
posi
tive
num
bers
m,
n, a
nd b
, w
here
b�
1,
of
Lo
gar
ith
ms
log b
�m n��
log b
m�
log b
n.
Po
wer
Pro
per
ty
For
any
rea
l num
ber
pan
d po
sitiv
e nu
mbe
rs m
and
b,
of
Lo
gar
ith
ms
whe
re b
�1,
log b
mp
�p
log b
m.
Use
log
328
3.
0331
an
d l
og3
4
1.26
19 t
o ap
pro
xim
ate
the
valu
e of
eac
h e
xpre
ssio
n.
a.lo
g 336
log 3
36�
log 3
(32
�4)
�lo
g 332
�lo
g 34
�2
�lo
g 34
2
�1.
2619
3.
2619
b.
log 3
7
log 3
7�
log 3
��
�lo
g 328
�lo
g 34
3.
0331
�1.
2619
1.
7712
c.lo
g 325
6
log 3
256
�lo
g 3(4
4 )�
4 �
log 3
4
4(1.
2619
)
5.04
76
28 � 4
Use
log
123
0.
4421
an
d l
og12
7
0.78
31 t
o ev
alu
ate
each
exp
ress
ion
.
1.lo
g 12
211.
2252
2.lo
g 12
0.34
103.
log 1
249
1.56
62
4.lo
g 12
361.
4421
5.lo
g 12
631.
6673
6.lo
g 12
�0.
2399
7.lo
g 12
0.20
228.
log 1
216
,807
3.91
559.
log 1
244
12.
4504
Use
log
53
0.
6826
an
d l
og5
4
0.86
14 t
o ev
alu
ate
each
exp
ress
ion
.
10.l
og5
121.
5440
11.l
og5
100
2.86
1412
.log
50.
75�
0.17
88
13.l
og5
144
3.08
8014
.log
50.
3250
15.l
og5
375
3.68
26
16.l
og5
1.3�
0.17
8817
.log
5�
0.35
7618
.log
51.
7304
81 � 59 � 1627 � 16
81 � 49
27 � 49
7 � 3
Exam
ple
Exer
cise
s
9-3
Cha
pter
920
Gle
ncoe
Alg
ebra
2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-3 i
n y
our
text
boo
k.
1.F
ind
the
valu
e of
eac
h o
f th
e fo
llow
ing.
a.lo
g 512
53
b.
log 5
51
c.lo
g 5(1
25
5)2
2.W
hic
h o
f th
e fo
llow
ing
stat
emen
ts i
s tr
ue?
BA
.lo
g 5(1
25
5) �
(log
512
5)
(log
55)
B.
log 5
(125
5)
�lo
g 512
5 �
log 5
5
Rea
d t
he
Less
on
1.E
ach
of
the
prop
erti
es o
f lo
gari
thm
s ca
n b
e st
ated
in
wor
ds o
r in
sym
bols
.Com
plet
e th
est
atem
ents
of
thes
e pr
oper
ties
in
wor
ds.
a.T
he
loga
rith
m o
f a
quot
ien
t is
th
e of
th
e lo
gari
thm
s of
th
e
and
the
.
b.
Th
e lo
gari
thm
of
a po
wer
is
the
of t
he
loga
rith
m o
f th
e ba
se a
nd
the
.
c.T
he
loga
rith
m o
f a
prod
uct
is
the
of t
he
loga
rith
ms
of i
ts
.
2.S
tate
wh
eth
er e
ach
of
the
foll
owin
g eq
uat
ion
s is
tru
eor
fal
se.I
f th
e st
atem
ent
is t
rue,
nam
e th
e pr
oper
ty o
f lo
gari
thm
s th
at i
s il
lust
rate
d.
a.lo
g 310
�lo
g 330
�lo
g 33
tru
e;Q
uo
tien
t P
rop
erty
b.l
og4
12 �
log 4
4 �
log 4
8fa
lse
c.lo
g 281
�2
log 2
9tr
ue;
Po
wer
Pro
per
tyd
.log
830
�lo
g 85
�lo
g 86
fals
e
3.T
he
alge
brai
c pr
oces
s of
sol
vin
g th
e eq
uat
ion
log
2x
�lo
g 2(x
�2)
�3
lead
s to
“x
��
4or
x�
2.”
Doe
s th
is m
ean
th
at b
oth
�4
and
2 ar
e so
luti
ons
of t
he
loga
rith
mic
equ
atio
n?
Exp
lain
you
r re
ason
ing.
Sam
ple
an
swer
:N
o;
2 is
a s
olu
tio
n b
ecau
se it
ch
ecks
:lo
g2
2 �
log
2(2
�2)
�lo
g2
2 �
log
24
�1
�2
�3.
Ho
wev
er,
bec
ause
log
2(�
4) a
nd
log
2(�
2) a
re u
nd
efin
ed,�
4 is
an
ext
ran
eou
sso
luti
on
an
d m
ust
be
elim
inat
ed.T
he
on
ly s
olu
tio
n is
2.
Rem
emb
er W
hat
Yo
u L
earn
ed4.
A g
ood
way
to
rem
embe
r so
met
hing
is
to r
elat
e it
som
ethi
ng y
ou a
lrea
dy k
now
.Use
wor
dsto
exp
lain
how
th
e P
rodu
ct P
rope
rty
for
expo
nen
ts c
an h
elp
you
rem
embe
r th
e pr
odu
ctpr
oper
ty f
or l
ogar
ith
ms.
Sam
ple
an
swer
:Wh
en y
ou
mu
ltip
lytw
o n
um
ber
s o
rex
pre
ssio
ns
wit
h t
he
sam
e b
ase,
you
ad
dth
e ex
po
nen
ts a
nd
kee
p t
he
sam
e b
ase.
Lo
gar
ith
ms
are
exp
on
ents
,so
to
fin
d t
he
log
arit
hm
of
ap
rod
uct
,yo
u a
dd
the
log
arit
hm
s o
f th
e fa
cto
rs,k
eep
ing
th
e sa
me
bas
e.
fact
ors
sum
exp
on
ent
pro
du
ctd
eno
min
ato
rn
um
erat
or
dif
fere
nce
Less
on R
eadi
ng G
uide
Pro
per
ties
of
Lo
gar
ith
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
9-3
Chapter 9 A10 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-3)
Skill
s Pr
acti
ceP
rop
erti
es o
f L
og
arit
hm
s
9-3
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
923
Gle
ncoe
Alg
ebra
2
Lesson 9-3
Use
log
23
1.
5850
an
d l
og2
5
2.32
19 t
o ap
pro
xim
ate
the
valu
e of
eac
hex
pre
ssio
n.
1.lo
g 225
4.64
382.
log 2
274.
755
3.lo
g 2�
0.73
694.
log 2
0.73
69
5.lo
g 215
3.90
696.
log 2
455.
4919
7.lo
g 275
6.22
888.
log 2
0.6
�0.
7369
9.lo
g 2�
1.58
5010
.log
20.
8481
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
11.l
og10
27 �
3 lo
g 10
x3
12.3
log
74
�2
log 7
b8
13.l
og4
5 �
log 4
x�
log 4
6012
14.l
og6
2c�
log 6
8 �
log 6
805
15.l
og5
y�
log 5
8 �
log 5
18
16.l
og2
q�
log 2
3 �
log 2
721
17.l
og9
4 �
2 lo
g 95
�lo
g 9w
100
18.3
log
82
�lo
g 84
�lo
g 8b
2
19.l
og10
x�
log 1
0(3
x�
5) �
log 1
02
220
.log
4x
�lo
g 4(2
x�
3) �
log 4
22
21.l
og3
d�
log 3
3 �
39
22.l
og10
y�
log 1
0(2
�y)
�0
1
23.l
og2
s�
2 lo
g 25
�0
24.l
og2
(x�
4) �
log 2
(x�
3) �
34
25.l
og4
(n�
1) �
log 4
(n�
2) �
13
26.l
og5
10 �
log 5
12 �
3 lo
g 52
�lo
g 5a
15
1 � 25
9 � 51 � 3
5 � 33 � 5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
Cha
pter
922
Gle
ncoe
Alg
ebra
2
Solv
e Lo
gar
ith
mic
Eq
uat
ion
sYo
u c
an u
se t
he
prop
erti
es o
f lo
gari
thm
s to
sol
veeq
uat
ion
s in
volv
ing
loga
rith
ms.
Sol
ve e
ach
eq
uat
ion
.
a.2
log 3
x�
log 3
4 �
log 3
25
2 lo
g 3x
�lo
g 34
�lo
g 325
Orig
inal
equ
atio
n
log 3
x2�
log 3
4 �
log 3
25P
ower
Pro
pert
y
log 3
�lo
g 325
Quo
tient
Pro
pert
y
�25
Pro
pert
y of
Equ
ality
for
Loga
rithm
ic F
unct
ions
x2�
100
Mul
tiply
eac
h si
de b
y 4.
x�
10
Take
the
squ
are
root
of
each
sid
e.
Sin
ce l
ogar
ith
ms
are
un
defi
ned
for
x�
0,�
10 i
s an
ext
ran
eou
s so
luti
on.
Th
e on
ly s
olu
tion
is
10.
b.
log 2
x�
log 2
(x�
2) �
3
log 2
x�
log 2
(x�
2) �
3O
rigin
al e
quat
ion
log 2
x(x
�2)
�3
Pro
duct
Pro
pert
y
x(x
�2)
�23
Def
initi
on o
f lo
garit
hm
x2�
2x�
8D
istr
ibut
ive
Pro
pert
y
x2�
2x �
8 �
0S
ubtr
act
8 fr
om e
ach
side
.
(x�
4)(x
�2)
�0
Fact
or.
x�
2or
x�
�4
Zer
o P
rodu
ct P
rope
rty
Sin
ce l
ogar
ith
ms
are
un
defi
ned
for
x�
0,�
4 is
an
ext
ran
eou
s so
luti
on.
Th
e on
ly s
olu
tion
is
2.
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
1.lo
g 54
�lo
g 52x
�lo
g 524
32.
3 lo
g 46
�lo
g 48
�lo
g 4x
27
3.lo
g 625
�lo
g 6x
�lo
g 620
44.
log 2
4 �
log 2
(x�
3) �
log 2
8�
5.lo
g 62x
�lo
g 63
�lo
g 6(x
�1)
36.
2 lo
g 4(x
�1)
�lo
g 4(1
1 �
x)2
7.lo
g 2x
�3
log 2
5 �
2 lo
g 210
12,5
008.
3 lo
g 2x
�2
log 2
5x�
210
0
9.lo
g 3(c
�3)
�lo
g 3(4
c�
1) �
log 3
510
.log
5(x
�3)
�lo
g 5(2
x�
1) �
24 � 7
8 � 19
5 � 21 � 2
x2� 4x2� 4
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Pro
per
ties
of
Lo
gar
ith
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
Exer
cise
s
Exam
ple
Chapter 9 A11 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-3)
9-3
Wor
d Pr
oble
m P
ract
ice
Pro
per
ties
of
Lo
gar
ith
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
925
Gle
ncoe
Alg
ebra
2
Lesson 9-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.M
ENTA
L C
OM
PUTA
TIO
NJe
ssic
a h
asm
emor
ized
log
52
0.
4307
an
d lo
g 53
0.
6826
.Usi
ng
this
in
form
atio
n,t
o th
en
eare
st t
hou
san
dth
,wh
at p
ower
of
5 is
equ
al t
o 6?
1.11
3
2.PO
WER
SA
ch
emis
t is
for
mu
lati
ng
anac
id.T
he
pH o
f a
solu
tion
is
give
n b
y
�lo
g 10
C,
wh
ere
C i
s th
e co
nce
ntr
atio
n o
fh
ydro
gen
ion
s.If
th
e co
nce
ntr
atio
n o
fh
ydro
gen
ion
s is
in
crea
sed
by a
fac
tor
of 1
00,w
hat
hap
pen
s to
th
e pH
of
the
solu
tion
?T
he
pH
dec
reas
es b
y 2.
3.LU
CK
Y M
ATH
Fra
nk
is s
olvi
ng
apr
oble
m i
nvo
lvin
g lo
gari
thm
s.H
e do
esev
eryt
hin
g co
rrec
tly
exce
pt f
or o
ne
thin
g.H
e m
ista
ken
ly w
rite
s
log 2
a�
log 2
b�
log 2
(a�
b).
How
ever
,aft
er s
ubs
titu
tin
g th
e va
lues
for
aan
d b
in h
is p
robl
em,h
e am
azin
gly
stil
l ge
ts t
he
righ
t an
swer
! Th
e va
lue
of a
was
11.
Wh
at m
ust
th
e va
lue
of b
hav
e be
en?
1.1
4.LE
NG
THS
Ch
arle
s h
as t
wo
pole
s.O
ne
pole
has
len
gth
equ
al t
o lo
g 721
an
d th
e ot
her
has
len
gth
equ
al t
o lo
g 725
.E
xpre
ss t
he
len
gth
of
both
pol
es jo
ined
end
to e
nd
as t
he
loga
rith
m o
f a
sin
gle
nu
mbe
r.lo
g7
525
SIZE
For
Exe
rcis
es 5
-7,u
se t
he
foll
owin
g in
form
atio
n.
Ali
cia
wan
ted
to t
ry t
o qu
anti
fy t
he
term
spu
ny,
tin
y,sm
all,
med
ium
,lar
ge,b
ig,h
uge
,an
d h
um
ongo
us.
Sh
e pi
cked
a n
um
ber
of o
bjec
ts a
nd
clas
sifi
ed t
hem
wit
h t
hes
ead
ject
ives
of
size
.Sh
e n
otic
ed t
hat
th
e sc
ale
seem
ed e
xpon
enti
al.T
her
efor
e,sh
e ca
me
up
wit
h t
he
foll
owin
g de
fin
itio
n.D
efin
e S
to b
e
log 3
V,w
her
e V
is v
olu
me
in c
ubi
c fe
et.
Th
en u
se t
he
foll
owin
g ta
ble
to f
ind
the
appr
opri
ate
adje
ctiv
e.
5.D
eriv
e an
exp
ress
ion
for
Sap
plie
d to
a
cube
in
ter
ms
of �
wh
ere
�is
th
e si
dele
ngt
h o
f a
cube
.lo
g3
�
6.H
ow m
any
cube
s,ea
ch o
ne
foot
on
a
side
,wou
ld h
ave
to b
e pu
t to
geth
er
to g
et a
n o
bjec
t th
at A
lici
a w
ould
cal
l“b
ig”?
729
7.H
ow l
ikel
y is
it
that
a l
arge
obj
ect
atta
ched
to
a bi
g ob
ject
wou
ld r
esu
lt i
n
a h
uge
obj
ect,
acco
rdin
g to
Ali
cia’
s sc
ale.
No
t ve
ry li
kely
;m
ost
like
ly t
he
resu
lt w
ill b
e b
ig,n
ot
hu
ge.
Ssa
tisf
ies
Ad
ject
ive
�2
�S
��
1tin
y
�1
�S
�0
smal
l
0 �
S�
1m
ediu
m
1 �
S�
2la
rge
2 �
S�
3bi
g
3 �
S�
4hu
ge
1 � 3
Prac
tice
Pro
per
ties
of
Lo
gar
ith
ms
9-3
Cha
pter
924
Gle
ncoe
Alg
ebra
2
Use
log
105
0.
6990
an
d l
og10
7
0.84
51 t
o ap
pro
xim
ate
the
valu
e of
eac
hex
pre
ssio
n.
1.lo
g 10
351.
5441
2.lo
g 10
251.
3980
3.lo
g 10
0.14
614.
log 1
0�
0.14
61
5.lo
g 10
245
2.38
926.
log 1
017
52.
2431
7.lo
g 10
0.2
�0.
6990
8.lo
g 10
0.55
29
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
9.lo
g 7n
�lo
g 78
410
.log
10u
�lo
g 10
48
11.l
og6
x�
log 6
9 �
log 6
546
12.l
og8
48 �
log 8
w�
log 8
412
13.l
og9
(3u
�14
) �
log 9
5 �
log 9
2u2
14.4
log
2x
�lo
g 25
�lo
g 240
53
15.l
og3
y�
�lo
g 316
�lo
g 364
16.l
og2
d�
5 lo
g 22
�lo
g 28
4
17.l
og10
(3m
�5)
�lo
g 10
m�
log 1
02
218
.log
10(b
�3)
�lo
g 10
b�
log 1
04
1
19.l
og8
(t�
10)
�lo
g 8(t
�1)
�lo
g 812
220
.log
3(a
�3)
�lo
g 3(a
�2)
�lo
g 36
0
21.l
og10
(r�
4) �
log 1
0r
�lo
g 10
(r�
1)2
22.l
og4
(x2
�4)
�lo
g 4(x
�2)
�lo
g 41
3
23.l
og10
4 �
log 1
0w
�2
2524
.log
8(n
�3)
�lo
g 8(n
�4)
�1
4
25.3
log
5(x
2�
9) �
6 �
0
426
.log
16(9
x�
5) �
log 1
6(x
2�
1) �
3
27.l
og6
(2x
�5)
�1
�lo
g 6(7
x�
10)
828
.log
2(5
y�
2) �
1 �
log 2
(1 �
2y)
0
29.l
og10
(c2
�1)
�2
�lo
g 10
(c�
1)10
130
.log
7x
�2
log 7
x�
log 7
3 �
log 7
726
31.S
OU
ND
Rec
all
that
th
e lo
udn
ess
Lof
a s
oun
d in
dec
ibel
s is
giv
en b
y L
�10
log
10R
,w
her
e R
is t
he
sou
nd’
s re
lati
ve i
nte
nsi
ty.I
f th
e in
ten
sity
of
a ce
rtai
n s
oun
d is
tri
pled
,by
how
man
y de
cibe
ls d
oes
the
sou
nd
incr
ease
?ab
ou
t 4.
8 d
b
32.E
AR
THQ
UA
KES
An
ear
thqu
ake
rate
d at
3.5
on
th
e R
ich
ter
scal
e is
fel
t by
man
y pe
ople
,an
d an
ear
thqu
ake
rate
d at
4.5
may
cau
se l
ocal
dam
age.
Th
e R
ich
ter
scal
e m
agn
itu
dere
adin
g m
is g
iven
by
m�
log 1
0x,
wh
ere
xre
pres
ents
th
e am
plit
ude
of
the
seis
mic
wav
eca
usi
ng
grou
nd
mot
ion
.How
man
y ti
mes
gre
ater
is
the
ampl
itu
de o
f an
ear
thqu
ake
that
mea
sure
s 4.
5 on
th
e R
ich
ter
scal
e th
an o
ne
that
mea
sure
s 3.
5?10
tim
es
1 � 2
1 � 41 � 3
3 � 22 � 3
25 � 75 � 77 � 5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
Chapter 9 A12 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lessons 9-3 and 9-4)
Less
on R
eadi
ng G
uide
Co
mm
on
Lo
gar
ith
ms
9-4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
927
Gle
ncoe
Alg
ebra
2
Lesson 9-4
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-4 i
n y
our
text
boo
k.
Wh
ich
su
bsta
nce
is
mor
e ac
idic
,mil
k or
tom
atoe
s? to
mat
oes
Rea
d t
he
Less
on
1.R
hon
da u
sed
the
foll
owin
g ke
ystr
okes
to
ente
r an
exp
ress
ion
on
her
gra
phin
g ca
lcu
lato
r:
17
Th
e ca
lcu
lato
r re
turn
ed t
he
resu
lt 1
.230
4489
21.
Wh
ich
of
the
foll
owin
g co
ncl
usi
ons
are
corr
ect?
a,c,
and
d
a.T
he
base
10
loga
rith
m o
f 17
is
abou
t 1.
2304
.
b.
Th
e ba
se 1
7 lo
gari
thm
of
10 i
s ab
out
1.23
04.
c.T
he
com
mon
log
arit
hm
of
17 i
s ab
out
1.23
0449
.
d.
101.
2304
4892
1is
ver
y cl
ose
to 1
7.
e.T
he
com
mon
log
arit
hm
of
17 i
s ex
actl
y 1.
2304
4892
1.
2.M
atch
eac
h e
xpre
ssio
n f
rom
th
e fi
rst
colu
mn
wit
h a
n e
xpre
ssio
n f
rom
th
e se
con
d co
lum
nth
at h
as t
he
sam
e va
lue.
a.lo
g 22
ivi.
log 4
1
b.
log
12 ii
iii
.log
28
c.lo
g 31
iii
i.lo
g 10
12
d.
log 5
viv
.log
55
e.lo
g 10
00ii
v.lo
g 0.
1
3.C
alcu
lato
rs d
o n
ot h
ave
keys
for
fin
din
g ba
se 8
log
arit
hm
s di
rect
ly.H
owev
er,y
ou c
an u
se
a ca
lcu
lato
r to
fin
d lo
g 820
if
you
app
ly t
he
form
ula
.
Wh
ich
of
the
foll
owin
g ex
pres
sion
s ar
e eq
ual
to
log 8
20?
B a
nd
C
A.l
og20
8B
.C
.D
.
Rem
emb
er W
hat
Yo
u L
earn
ed
4.S
omet
imes
it
is e
asie
r to
rem
embe
r a
form
ula
if
you
can
sta
te i
t in
wor
ds.S
tate
th
ech
ange
of
base
for
mu
la i
n w
ords
.S
amp
le a
nsw
er:T
o c
han
ge
the
log
arit
hm
of
an
um
ber
fro
m o
ne
bas
e to
an
oth
er,d
ivid
e th
e lo
g o
f th
e o
rig
inal
nu
mb
erin
th
e o
ld b
ase
by t
he
log
of
the
new
bas
e in
th
e o
ld b
ase.
log
8� lo
g 20
log
20� lo
g 8
log 10
20� lo
g 108
chan
ge
of
bas
e
1 � 5
ENTE
R)
LO
G
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
9-3
Cha
pter
926
Gle
ncoe
Alg
ebra
2
Sp
iral
sC
onsi
der
an a
ngl
e in
sta
nda
rd p
osit
ion
wit
h i
ts v
erte
x at
a p
oin
t O
call
ed t
he
pole
.Its
in
itia
l si
de i
s on
a c
oord
inat
ized
axi
s ca
lled
th
e po
lar
axis
.A p
oin
t P
on t
he
term
inal
sid
e of
th
e an
gle
is n
amed
by
the
pola
r co
ord
inat
es(r
,�),
wh
ere
ris
th
e di
rect
ed d
ista
nce
of
the
poin
t fr
om O
and
�is
th
e m
easu
re o
fth
e an
gle.
Gra
phs
in t
his
sys
tem
may
be
draw
n o
n p
olar
coo
rdin
ate
pape
rsu
ch a
s th
e ki
nd
show
n b
elow
.
1.U
se a
cal
cula
tor
to c
ompl
ete
the
tabl
e fo
r lo
g 2r
�� 12�
0�.
(Hin
t:T
o fi
nd
�on
a c
alcu
lato
r,pr
ess
120
r2
.)
2.P
lot
the
poin
ts f
oun
d in
Exe
rcis
e 1
on t
he
grid
abo
ve a
nd
con
nec
t to
fo
rm a
sm
ooth
cu
rve.
Th
is t
ype
of s
pira
l is
cal
led
a lo
gari
thm
ic s
pira
l be
cau
se t
he
angl
e m
easu
res
are
prop
orti
onal
to
the
loga
rith
ms
of t
he
radi
i.
r1
23
45
67
8
�0�
120�
190�
240�
279�
310�
337�
360�
)
LOG
�)
LO
G�
01020
30
40
5060
7080
9010
011
012
013
0
140
150
160
170
180
190 200 21
0 220 23
0
240
250
260
270
280
290
300
310
32033
0340350
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
9-3
Chapter 9 A13 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-4)
9-4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
929
Gle
ncoe
Alg
ebra
2
Lesson 9-4
Ch
ang
e o
f B
ase
Form
ula
Th
e fo
llow
ing
form
ula
is
use
d to
ch
ange
exp
ress
ion
s w
ith
diff
eren
t lo
gari
thm
ic b
ases
to
com
mon
log
arit
hm
exp
ress
ion
s.
Ch
ang
e o
f B
ase
Fo
rmu
laF
or a
ll po
sitiv
e nu
mbe
rs a
, b,
and
n,
whe
re a
�1
and
b�
1, lo
g an
�
Exp
ress
log
815
in
ter
ms
of c
omm
on l
ogar
ith
ms.
Th
en a
pp
roxi
mat
eit
s va
lue
to f
our
dec
imal
pla
ces.
log 8
15�
Cha
nge
of B
ase
For
mul
a
1.
3023
Sim
plify
.
Th
e va
lue
of l
og8
15 i
s ap
prox
imat
ely
1.30
23.
Exp
ress
eac
h l
ogar
ith
m i
n t
erm
s of
com
mon
log
arit
hm
s.T
hen
ap
pro
xim
ate
its
valu
e to
fou
r d
ecim
al p
lace
s.
1.lo
g 316
2.lo
g 240
3.lo
g 535
,2.5
237
,5.3
219
,2.2
091
4.lo
g 422
5.lo
g 12
200
6.lo
g 250
,2.2
297
,2.1
322
,5.6
439
7.lo
g 50.
48.
log 3
29.
log 4
28.5
,�0.
5693
,0.6
309
,2.4
164
10.l
og3
(20)
211
.log
6(5
)412
.log
8(4
)5
,5.4
537
,3.5
930
,3.3
333
13.l
og5
(8)3
14.l
og2
(3.6
)615
.log
12(1
0.5)
4
,3.8
761
,11.
0880
,3.7
851
16.l
og3
�15
0�
17.l
og4
3 �39�
18.l
og5
4 �16
00�
,2.2
804
,0.8
809
,1.1
460
log
160
0�
�4
log
5lo
g 3
9� 3
log
4lo
g 1
50� 2
log
3
4 lo
g 1
0.5
��
log
12
6 lo
g 3
.6�
�lo
g 2
3 lo
g 8
�lo
g 5
5 lo
g 4
�lo
g 8
4 lo
g 5
�lo
g 6
2 lo
g 2
0�
�lo
g 3
log
28.
5�
�lo
g 4
log
2� lo
g 3
log
0.4
�lo
g 5
log
50
� log
2lo
g 2
00� lo
g 1
2lo
g 2
2� lo
g 4
log
35
� log
5lo
g 4
0� lo
g 2
log
16
� log
3
log 10
15� lo
g 108
log b
n� lo
g ba
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(con
tinued
)
Co
mm
on
Lo
gar
ith
ms
Exer
cise
s
Exam
ple
9-4
Cha
pter
928
Gle
ncoe
Alg
ebra
2
Co
mm
on
Lo
gar
ith
ms
Bas
e 10
log
arit
hm
s ar
e ca
lled
com
mon
log
arit
hm
s.T
he
expr
essi
on l
og10
xis
usu
ally
wri
tten
wit
hou
t th
e su
bscr
ipt
as l
og x
.Use
th
e ke
y on
you
r ca
lcu
lato
r to
eva
luat
e co
mm
on l
ogar
ith
ms.
Th
e re
lati
on b
etw
een
exp
onen
ts a
nd
loga
rith
ms
give
s th
e fo
llow
ing
iden
tity
.
Inve
rse
Pro
per
ty o
f L
og
arit
hm
s an
d E
xpo
nen
ts10
log
x�
x
Eva
luat
e lo
g 50
to
fou
r d
ecim
al p
lace
s.U
se t
he
LO
G k
ey o
n y
our
calc
ula
tor.
To
fou
r de
cim
al p
lace
s,lo
g 50
�1.
6990
.
Sol
ve 3
2x�
1�
12.
32x
�1
�12
Orig
inal
equ
atio
n
log
32x
�1
�lo
g 12
Pro
pert
y of
Equ
ality
for
Loga
rithm
s
(2x
�1)
log
3 �
log
12P
ower
Pro
pert
y of
Log
arith
ms
2x�
1 �
Div
ide
each
sid
e by
log
3.
2x�
�1
Sub
trac
t 1
from
eac
h si
de.
x�
��
1 �M
ultip
ly e
ach
side
by
.
x
0.63
09
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.lo
g 18
2.lo
g 39
3.lo
g 12
01.
2553
1.59
112.
0792
4.lo
g 5.
85.
log
42.3
6.lo
g 0.
003
0.76
341.
6263
�2.
5229
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Rou
nd
to
fou
r d
ecim
al p
lace
s.
7.43
x�
120.
5975
8.6x
�2
�18
�0.
3869
9.54
x�
2�
120
1.24
3710
.73x
�1
�21
{x|x
0.
8549
}
11.2
.4x
�4
�30
�0.
1150
12.6
.52x
�20
0{x
|x
1.41
53}
13.3
.64x
�1
�85
.41.
1180
14.2
x�
5�
3x�
213
.966
6
15.9
3x�
45x
�2
�8.
1595
16.6
x�
5�
27x
�3
�3.
60691 � 2
log
12� lo
g 3
1 � 2
log
12� lo
g 3
log
12� lo
g 3
LOG
Stud
y G
uide
and
Inte
rven
tion
C
om
mo
n L
og
arit
hm
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-4
Exer
cise
s
Exam
ple
1
Exam
ple
2
Chapter 9 A14 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-4)
9-4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
931
Gle
ncoe
Alg
ebra
2
Lesson 9-4
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.lo
g 10
12.
0043
2.lo
g 2.
20.
3424
3.lo
g 0.
05�
1.30
10
Use
th
e fo
rmu
la p
H �
�lo
g[H
�]
to f
ind
th
e p
H o
f ea
ch s
ub
stan
ce g
iven
its
con
cen
trat
ion
of
hyd
roge
n i
ons.
4.m
ilk:
[H�
] �
2.51
�10
�7
mol
e pe
r li
ter
6.6
5.ac
id r
ain
:[H
�]
�2.
51 �
10�
6m
ole
per
lite
r5.
6
6.bl
ack
coff
ee:[
H�
] �
1.0
�10
�5
mol
e pe
r li
ter
5.0
7.m
ilk
of m
agn
esia
:[H
�]
�3.
16 �
10�
11m
ole
per
lite
r10
.5
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Rou
nd
to
fou
r d
ecim
al p
lace
s.
8.2x
�25
{x|x
�4.
6439
}9.
5a�
120
2.97
4610
.6z
�45
.62.
1319
11.9
m�
100
{m|m
2.
0959
}12
.3.5
x�
47.9
3.08
8513
.8.2
y�
64.5
1.98
02
14.2
b�
1�
7.31
{b|b
�1.
8699
}15.
42x
�27
1.18
8716
.2a
�4
�82
.110
.359
3
17.9
z�
2�
38{z
|z�
3.65
55}
18.5
w�
3�
17�
1.23
9619
.30x
2�
50
1.07
25
20.5
x2�
3�
72
2.37
8521
.42x
�9x
�1
3.81
8822
.2n
�1
�52
n�
10.
9117
Exp
ress
eac
h l
ogar
ith
m i
n t
erm
s of
com
mon
log
arit
hm
s.T
hen
ap
pro
xim
ate
its
valu
e to
fou
r d
ecim
al p
lace
s.
23.l
og5
12;
1.54
4024
.log
832
;1.
6667
25.l
og11
9 ;
0.91
63
26.l
og2
18
;4.
1699
27.l
og9
6;
0.81
5528
.log
7�
8�;
29.H
OR
TIC
ULT
UR
ES
iber
ian
iri
ses
flou
rish
wh
en t
he
con
cen
trat
ion
of
hyd
roge
n i
ons
[H�
]in
th
e so
il i
s n
ot l
ess
than
1.5
8 �
10�
8m
ole
per
lite
r.W
hat
is
the
pH o
f th
e so
il i
n w
hic
hth
ese
iris
es w
ill
flou
rish
?7.
8 o
r le
ss
30.A
CID
ITY
Th
e pH
of
vin
egar
is
2.9
and
the
pH o
f m
ilk
is 6
.6.H
ow m
any
tim
es g
reat
er i
sth
e h
ydro
gen
ion
con
cen
trat
ion
of
vin
egar
th
an o
f m
ilk?
abo
ut
5000
31.B
IOLO
GY
Th
ere
are
init
iall
y 10
00 b
acte
ria
in a
cu
ltu
re.T
he
nu
mbe
r of
bac
teri
a do
ubl
esea
ch h
our.
Th
e n
um
ber
of b
acte
ria
Npr
esen
t af
ter
th
ours
is
N�
1000
(2)t
.How
lon
g w
ill
it t
ake
the
cult
ure
to
incr
ease
to
50,0
00 b
acte
ria?
abo
ut
5.6
h
32.S
OU
ND
An
equ
atio
n f
or l
oudn
ess
Lin
dec
ibel
s is
giv
en b
y L
�10
log
R,w
her
e R
is t
he
sou
nd’
s re
lati
ve i
nte
nsi
ty.A
n a
ir-r
aid
sire
n c
an r
each
150
dec
ibel
s an
d je
t en
gin
e n
oise
can
rea
ch 1
20 d
ecib
els.
How
man
y ti
mes
gre
ater
is
the
rela
tive
in
ten
sity
of
the
air-
raid
sire
n t
han
th
at o
f th
e je
t en
gin
e n
oise
?10
00
log
108
� 2 lo
g10
7lo
g10
6�
�lo
g10
9lo
g10
18�
�lo
g10
2
log
109
��
log
1011
log
1032
��
log
108
log
1012
��
log
105
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.53
43
Prac
tice
C
om
mo
n L
og
arit
hm
s
9-4
Cha
pter
930
Gle
ncoe
Alg
ebra
2
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.lo
g 6
0.77
822.
log
151.
1761
3.lo
g 1.
10.
0414
4.lo
g 0.
3�
0.52
29
Use
th
e fo
rmu
la p
H �
�lo
g[H
�]
to f
ind
th
e p
H o
f ea
ch s
ub
stan
ce g
iven
its
con
cen
trat
ion
of
hyd
roge
n i
ons.
5.ga
stri
c ju
ices
:[H
�]
�1.
0 �
10�
1m
ole
per
lite
r1.
0
6.to
mat
o ju
ice:
[H�
] �
7.94
�10
�5
mol
e pe
r li
ter
4.1
7.bl
ood:
[H�
] �
3.98
�10
�8
mol
e pe
r li
ter
7.4
8.to
oth
past
e:[H
�]
�1.
26 �
10�
10m
ole
per
lite
r9.
9
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
Rou
nd
to
fou
r d
ecim
al p
lace
s.
9.3x
�24
3{x
|x�
5}10
.16v
��v �
v�
��
11.8
p�
501.
8813
12.7
y�
151.
3917
13.5
3b�
106
0.96
5914
.45k
�37
0.52
09
15.1
27p
�12
00.
2752
16.9
2m�
270.
75
17.3
r�
5�
4.1
6.28
4318
.8y
�4
�15
{y|y
��
2.69
77}
19.7
.6d
�3
�57
.2�
1.00
4820
.0.5
t�
8�
16.3
3.97
32
21.4
2x2
�84
1.
0888
22.5
x2�
1 �10
0.
6563
Exp
ress
eac
h l
ogar
ith
m i
n t
erm
s of
com
mon
log
arit
hm
s.T
hen
ap
pro
xim
ate
its
valu
e to
fou
r d
ecim
al p
lace
s.
23.l
og3
7;
1.77
1224
.log
566
;2.
6032
25.l
og2
35;
5.12
9326
.log
610
;1.
2851
log
1010
��
log
106
log
1035
��
log
102
log
1066
��
log
105
log
107
� log
103
1 � 21 � 4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-4
9-4
Skill
s Pr
acti
ceC
om
mo
n L
og
arit
hm
s
Chapter 9 A15 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-4)
9-4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
933
Gle
ncoe
Alg
ebra
2
Lesson 9-4
Th
e S
lide
Ru
leB
efor
e th
e in
ven
tion
of
elec
tron
ic c
alcu
lato
rs,c
ompu
tati
ons
wer
e of
ten
perf
orm
ed o
n a
sli
de r
ule
.A s
lide
ru
le i
s ba
sed
on t
he
idea
of
loga
rith
ms.
It h
astw
o m
ovab
le r
ods
labe
led
wit
h C
an
d D
sca
les.
Eac
h o
f th
e sc
ales
is
loga
rith
mic
.
To
mu
ltip
ly 2
�3
on a
sli
de r
ule
,mov
e th
e C
rod
to
the
righ
t as
sh
own
belo
w.Y
ou c
an f
ind
2 �
3 by
add
ing
log
2 to
log
3,a
nd
the
slid
e ru
le a
dds
the
len
gth
s fo
r yo
u.T
he
dist
ance
you
get
is
0.77
8,or
th
e lo
gari
thm
of
6.
Fol
low
th
e st
eps
to m
ake
a sl
ide
rule
.
1.U
se g
raph
pap
er t
hat
has
sm
all
squ
ares
,su
ch a
s 10
squ
ares
to
the
inch
.Usi
ng
the
scal
es s
how
n a
t th
e ri
ght,
plot
th
e cu
rve
y�
log
xfo
r x
�1,
1.5,
and
the
wh
ole
nu
mbe
rs f
rom
2 t
hro
ugh
10.
Mak
e an
obv
iou
s h
eavy
dot
for
eac
h p
oin
t pl
otte
d.
2.Yo
u w
ill
nee
d tw
o st
rips
of
card
boar
d.A
5-
by-7
in
dex
card
,cu
t in
hal
f th
e lo
ng
way
,w
ill
wor
k fi
ne.
Tu
rn t
he
grap
h y
ou m
ade
in
Exe
rcis
e 1
side
way
s an
d u
se i
t to
mar
ka
loga
rith
mic
sca
le o
n e
ach
of
the
two
stri
ps.T
he
figu
re s
how
s th
e m
ark
for
2 be
ing
draw
n.
3.E
xpla
in h
ow t
o u
se a
sli
de r
ule
to
divi
de 8
by
2.L
ine
up
th
e 2
on
th
e C
sca
le w
ith
th
e 8
on
th
e D
sca
le.T
he
qu
oti
ent
is t
he
nu
mb
er o
n t
he
D s
cale
bel
ow
th
e 1
on
th
e C
sca
le.
0
0.1
0.2
0.3
y
1 2
11.
52
y =
log
x
0.1
0.2
12
1 21
CD
2 4
3 6
45
67
89
83
57
9
log
6
log
3lo
g 2
12
34
56
78
9
12
34
56
78
9
C D
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
1–2.
See
st
ud
ents
’wo
rk.
9-4
Cha
pter
932
Gle
ncoe
Alg
ebra
2
Wor
d Pr
oble
m P
ract
ice
Co
mm
on
Lo
gar
ith
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.O
THER
BA
SES
Jam
ie n
eeds
to
figu
reou
t w
hat
log
23
is,b
ut
she
only
has
a
tabl
e of
com
mon
log
arit
hm
s.In
th
eta
ble,
she
fin
ds t
hat
log
102
0.
3010
and
log 1
03
0.
4771
.Usi
ng
this
info
rmat
ion
,to
the
nea
rest
th
ousa
ndt
h,
wh
at i
s lo
g 23?
1.58
5
2.PH
Th
e pH
of
a so
luti
on i
s gi
ven
by
�lo
g 10
C,
wh
ere
C i
s th
e co
nce
ntr
atio
n o
fh
ydro
gen
ion
s in
mol
es p
er l
iter
.Aso
luti
on o
f ba
kin
g so
da c
reat
es a
hyd
roge
n i
on c
once
ntr
atio
n 5
�10
�9
of m
ole
per
lite
r.W
hat
is
the
pH o
f a
solu
tion
of
baki
ng
soda
? R
oun
d yo
ur
answ
er t
o th
e n
eare
st t
enth
.8.
3
3.G
RA
PHIN
GT
he
grap
h o
f y
�lo
g 10
xis
sh
own
bel
ow.U
se t
he
fact
th
at
3.
32 t
o sk
etch
a g
raph
of
y=
log 2
xon
th
e sa
me
grap
h.
O456 3 12
2040
6080
100
120
y
x
1� lo
g 102
4.SC
IEN
TIFI
C N
OTA
TIO
NW
hen
an
um
ber
nis
wri
tten
in
sci
enti
fic
not
atio
n,i
t h
as t
he
form
n�
s�
10p ,
wh
ere
sis
a n
um
ber
grea
ter
than
or
equ
al t
o 1
and
less
th
an 1
0 an
d p
is a
nin
tege
r.S
how
th
at p
�lo
g 10
n�
p�
1.n
�s
�10
p
log
10n
�lo
g10
(s�
10p
)�
log
10s
�lo
g10
10p
�lo
g10
s�
pB
ecau
se 1
�s
�10
,0
�lo
g10
s�
1.T
her
efo
re,p
�lo
g10
n�
p�
1.
LOG
TA
BLE
For
Exe
rcis
es 5
an
d 6
,use
the
foll
owin
g in
form
atio
n.
Mar
jori
e is
loo
kin
g th
rou
gh s
ome
old
scie
nce
boo
ks o
wn
ed b
y h
er g
ran
dfat
her
.A
t th
e ba
ck o
f on
e of
th
em,t
her
e is
a t
able
of l
ogar
ith
ms
base
10.
How
ever
,th
e bo
ok
is w
orn
ou
t an
d so
me
of t
he
entr
ies
are
un
read
able
.
5.A
ppro
xim
atel
y w
hat
are
th
e m
issi
ng
entr
ies
in t
he
tabl
e?
Rou
nd
off
you
ran
swer
s to
th
e n
eare
st t
hou
san
dth
.lo
g10
4
0.60
2lo
g10
6
0.77
8
6.H
ow c
an y
ou u
se t
his
tab
le t
o de
term
ine
log 1
01.
5?S
amp
le a
nsw
er:
log
101.
5�
log
103
�lo
g10
5 �
log
1010
0.
4771
�0.
6989
�1
�0.
1760
Tab
le o
f C
om
mo
n L
og
arit
hm
s(4
dec
imal
pla
ces
of
accu
racy
)
xlo
g 10
x
20.
3010
30.
4771
4?
50.
6989
6?
Chapter 9 A16 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-5)
9-5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
935
Gle
ncoe
Alg
ebra
2
Lesson 9-5
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
Th
e ir
rati
onal
nu
mbe
r e
2.
7182
8… o
ften
occ
urs
as t
he
base
for
exp
onen
tial
an
d lo
gari
thm
ic f
un
ctio
ns
that
des
crib
e re
al-w
orld
ph
enom
ena.
Nat
ura
l Bas
e e
As
nin
crea
ses,
�1 �
�nap
proa
ches
e
2.71
828…
.
ln x
�lo
g ex
Th
e fu
nct
ion
s y
�ex
and
y�
ln x
are
inve
rse
fun
ctio
ns.
Inve
rse
Pro
per
ty o
f B
ase
ean
d N
atu
ral L
og
arit
hm
sel
n x
�x
ln e
x�
x
Nat
ura
l ba
se e
xpre
ssio
ns
can
be
eval
uat
ed u
sin
g th
e ex
and
ln k
eys
on y
our
calc
ula
tor.
Eva
luat
e ln
168
5.U
se a
cal
cula
tor.
ln 1
685
7.
4295
Wri
te a
log
arit
hm
ic e
qu
atio
n e
qu
ival
ent
to e
2x�
7.e2
x�
7 →
log e
7 �
2xor
2x
�ln
7
Eva
luat
e ln
e18
.U
se t
he
Inve
rse
Pro
pert
y of
Bas
e e
and
Nat
ura
l L
ogar
ith
ms.
ln e
18�
18
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.ln
732
2.ln
84,
350
3.ln
0.7
354.
ln 1
006.
5958
11.3
427
�0.
3079
4.60
52
5.ln
0.0
824
6.ln
2.3
887.
ln 1
28,2
458.
ln 0
.006
14�
2.49
620.
8705
11.7
617
�5.
0929
Wri
te a
n e
qu
ival
ent
exp
onen
tial
or
loga
rith
mic
eq
uat
ion
.
9.e1
5�
x10
.e3x
�45
11.l
n 2
0 �
x12
.ln
x�
8ln
x�
153x
�ln
45
ex
�20
x�
e8
13.e
�5x
�0.
214
.ln
(4x
) �
9.6
15.e
8.2
�10
x16
.ln
0.0
002
�x
�5x
�ln
0.2
4x�
e9.
6ln
10x
�8.
2e
x�
0.00
02
Eva
luat
e ea
ch e
xpre
ssio
n.
17.l
n e
318
.eln
42
19.e
ln 0
.520
.ln
e16
.2
342
0.5
16.2
1 � n
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1
Exam
ple
2
Exam
ple
3Stud
y G
uide
and
Inte
rven
tion
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
9-5
Cha
pter
934
Gle
ncoe
Alg
ebra
2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-5 i
n y
our
text
boo
k.
Su
ppos
e th
at y
ou d
epos
it $
675
in a
sav
ings
acc
oun
t th
at p
ays
an a
nn
ual
in
tere
st r
ate
of 5
%.I
n e
ach
cas
e li
sted
bel
ow,i
ndi
cate
wh
ich
met
hod
of
com
pou
ndi
ng
wou
ld r
esu
lt
in m
ore
mon
ey i
n y
our
acco
un
t at
th
e en
d of
on
e ye
ar.
a.an
nu
al c
ompo
un
din
g or
mon
thly
com
pou
ndi
ng
mo
nth
lyb
.qu
arte
rly
com
pou
ndi
ng
or d
aily
com
pou
ndi
ng
dai
lyc.
dail
y co
mpo
un
din
g or
con
tin
uou
s co
mpo
un
din
gco
nti
nu
ou
s
Rea
d t
he
Less
on
1.Ja
gdis
h e
nte
red
the
foll
owin
g ke
ystr
okes
in
his
cal
cula
tor:
5
Th
e ca
lcu
lato
r re
turn
ed t
he
resu
lt 1
.609
4379
12.W
hic
h o
f th
e fo
llow
ing
con
clu
sion
s ar
eco
rrec
t?d
an
d f
a.T
he
com
mon
log
arit
hm
of
5 is
abo
ut
1.60
94.
b.
Th
e n
atu
ral
loga
rith
m o
f 5
is e
xact
ly 1
.609
4379
12.
c.T
he
base
5 l
ogar
ith
m o
f e
is a
bou
t 1.
6094
.
d.
Th
e n
atu
ral
loga
rith
m o
f 5
is a
bou
t 1.
6094
38.
e.10
1.60
9437
912
is v
ery
clos
e to
5.
f.e1
.609
4379
12is
ver
y cl
ose
to 5
.
2.M
atch
eac
h e
xpre
ssio
n f
rom
th
e fi
rst
colu
mn
wit
h i
ts v
alu
e in
th
e se
con
d co
lum
n.S
ome
choi
ces
may
be
use
d m
ore
than
on
ce o
r n
ot a
t al
l.
a.el
n 5
IVI.
1
b.
ln 1
VII
.10
c.el
n e
VI
III.
�1
d.
ln e
5IV
IV.5
e.ln
eI
V.0
f.ln
��I
IIV
I.e
Rem
emb
er W
hat
Yo
u L
earn
ed
3.A
goo
d w
ay t
o re
mem
ber
som
ethi
ng i
s to
exp
lain
it
to s
omeo
ne e
lse.
Sup
pose
tha
t yo
u ar
est
udy
ing
wit
h a
cla
ssm
ate
wh
o is
pu
zzle
d w
hen
ask
ed t
o ev
alu
ate
ln e
3 .H
ow w
ould
you
expl
ain
to
him
an
eas
y w
ay t
o fi
gure
th
is o
ut?
Sam
ple
an
swer
:ln
mea
ns
nat
ura
llo
g.T
he
nat
ura
l lo
g o
f e
3is
th
e p
ow
er t
o w
hic
h y
ou
rai
se e
to g
et e
3 .T
his
is o
bvio
usl
y 3.
1 � e
ENTE
R)
LN
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
9-5
Less
on R
eadi
ng G
uide
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
Chapter 9 A17 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-5)
9-5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
937
Gle
ncoe
Alg
ebra
2
Lesson 9-5
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.e3
20.0
855
2.e�
20.
1353
3.ln
20.
6931
4.ln
0.0
9�
2.40
79
Wri
te a
n e
qu
ival
ent
exp
onen
tial
or
loga
rith
mic
eq
uat
ion
.
5.ex
�3
x�
ln 3
6.e4
�8x
4 �
ln 8
x
7.ln
15
�x
ex
�15
8.ln
x
0.69
31x
e0
.693
1
Eva
luat
e ea
ch e
xpre
ssio
n.
9.el
n 3
310
.eln
2x
2x
11.l
n e
�2.
5�
2.5
12.l
n e
yy
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
13.e
x�
5{x
|x
1.60
94}
14.e
x�
3.2
{x|x
�1.
1632
}
15.2
ex�
1 �
111.
7918
16.5
ex�
3 �
181.
0986
17.e
3x�
301.
1337
18.e
�4x
�10
{x|x
��
0.57
56}
19.e
5x�
4 �
34{x
|x�
0.68
02}
20.1
�2e
2x�
�19
1.15
13
21.l
n 3
x�
22.
4630
22.l
n 8
x�
32.
5107
23.l
n (
x�
2) �
29.
3891
24.l
n (
x�
3) �
1�
0.28
17
25.l
n (
x�
3) �
451
.598
226
.ln
x�
ln 2
x�
21.
9221
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceB
ase
e an
d N
atu
ral L
og
arit
hm
s
9-5
Cha
pter
936
Gle
ncoe
Alg
ebra
2
Equ
atio
ns
and
Ineq
ual
itie
s w
ith
ean
d ln
All
pro
pert
ies
of l
ogar
ith
ms
from
earl
ier
less
ons
can
be
use
d to
sol
ve e
quat
ion
s an
d in
equ
alit
ies
wit
h n
atu
ral
loga
rith
ms.
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
a.3e
2x�
2 �
103e
2x�
2 �
10O
rigin
al e
quat
ion
3e2x
�8
Sub
trac
t 2
from
eac
h si
de.
e2x
�D
ivid
e ea
ch s
ide
by 3
.
ln e
2x�
ln
Pro
pert
y of
Equ
ality
for
Loga
rithm
s
2x�
ln
Inve
rse
Pro
pert
y of
Exp
onen
ts a
nd L
ogar
ithm
s
x�
ln
Mul
tiply
eac
h si
de b
y �1 2� .
x
0.49
04U
se a
cal
cula
tor.
b.
ln (
4x�
1) �
2
ln (
4x�
1) �
2O
rigin
al in
equa
lity
eln
(4x
�1)
�e2
Writ
e ea
ch s
ide
usin
g ex
pone
nts
and
base
e.
0 �
4x�
1 �
e2In
vers
e P
rope
rty
of E
xpon
ents
and
Log
arith
ms
1 �
4x�
e2�
1A
dditi
on P
rope
rty
of I
nequ
aliti
es
�x
�(e
2�
1)M
ultip
licat
ion
Pro
pert
y of
Ine
qual
ities
0.25
�x
�2.
0973
Use
a c
alcu
lato
r.
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
1.e4
x�
120
2.ex
�25
3.ex
�2
�4
�21
1.19
69{x
|x�
3.21
89}
4.83
32
4.ln
6x
�4
5.ln
(x
�3)
�5
��
26.
e�8x
�50
x
9.09
9717
.085
5{x
|x
�0.
4890
}
7.e4
x�
1�
3 �
128.
ln (
5x�
3) �
3.6
9.2e
3x�
5 �
20.
9270
6.71
96n
o s
olu
tio
n
10.6
�3e
x�
1�
2111
.ln
(2x
�5)
�8
12.l
n 5
x�
ln 3
x�
90.
6094
1492
.979
0{x
|x�
23.2
423}
1 � 41 � 4
8 � 31 � 2
8 � 38 � 3
8 � 3
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
9-5
Exer
cise
s
Exam
ple
Stud
y G
uide
and
Inte
rven
tion
(con
tinued
)
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
Chapter 9 A18 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-5)
9-5
Wor
d Pr
oble
m P
ract
ice
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
939
Gle
ncoe
Alg
ebra
2
Lesson 9-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.IN
TER
EST
Hor
atio
ope
ns
a ba
nk
acco
un
t th
at p
ays
2.3%
an
nu
al i
nte
rest
com
pou
nde
d co
nti
nu
ousl
y.H
e m
akes
an
init
ial
depo
sit
of 1
0,00
0.W
hat
wil
l be
the
bala
nce
of
the
acco
un
t in
10
year
s?A
ssu
me
that
he
mak
es n
o ad
diti
onal
depo
sits
an
d n
o w
ith
draw
als.
$12,
586
2.IN
TER
EST
Jan
ie’s
ban
k pa
ys 2
.8%
ann
ual
in
tere
st c
ompo
un
ded
con
tin
uou
sly
on s
avin
gs a
ccou
nts
.S
he
plac
ed $
2000
in
th
e ac
cou
nt.
How
lon
g w
ill
it t
ake
for
her
in
itia
l de
posi
t to
dou
ble
in v
alu
e? A
ssu
me
that
sh
em
akes
no
addi
tion
al d
epos
its
and
no
wit
hdr
awal
s.R
oun
d yo
ur
answ
er t
o th
en
eare
st q
uar
ter
year
.24
.75
yr
3.B
AC
TER
IAA
bac
teri
al p
opu
lati
ongr
ows
expo
nen
tial
ly,d
oubl
ing
ever
y 72
hou
rs.L
et P
be t
he
init
ial
popu
lati
onsi
ze a
nd
let
tbe
tim
e in
hou
rs.W
rite
a
form
ula
usi
ng
the
nat
ura
l ba
seex
pon
enti
al f
un
ctio
n t
hat
giv
es t
he
size
of
the
popu
lati
on a
s a
fun
ctio
n
of P
and
t.
P�
e
4.PO
PULA
TIO
NT
he
equ
atio
n A
�A
0er
t
desc
ribe
s th
e gr
owth
of
the
wor
ld’s
popu
lati
on w
her
e A
is t
he
popu
lati
on
at t
ime
t,A
0is
th
e po
pula
tion
at
t�
0,an
d r
is t
he
ann
ual
gro
wth
rat
e.H
owlo
ng
wil
l ta
ke a
pop
ula
tion
of
6.5
bill
ion
to i
ncr
ease
to
9 bi
llio
n i
f th
e an
nu
algr
owth
rat
e is
2%
? 16
.3 y
r�ln 722 �
t
MO
NEY
MA
NA
GEM
ENT
For
Exe
rcis
es5–
7,u
se t
he
foll
owin
g in
form
atio
n.
Lin
da w
ants
to
inve
st $
20,0
00.S
he
islo
okin
g at
tw
o po
ssib
le a
ccou
nts
.Acc
oun
t A
is a
sta
nda
rd s
avin
gs a
ccou
nt
that
pay
s3.
4% a
nn
ual
in
tere
st c
ompo
un
ded
con
tin
uou
sly.
Acc
oun
t B
wou
ld p
ay h
er
a fi
xed
amou
nt
of $
200
ever
y qu
arte
r.
5.If
Lin
da c
an i
nve
st t
he
mon
ey f
or
5 ye
ars
only
,wh
ich
acc
oun
t w
ould
gi
ve h
er t
he
hig
her
ret
urn
on
her
inve
stm
ent?
How
mu
ch m
ore
mon
eyw
ould
sh
e m
ake
by c
hoo
sin
g th
e h
igh
erpa
yin
g ac
cou
nt?
Acc
ou
nt
B;
she’
ll m
ake
$240
00 �
$237
06.1
0 �
$293
.90
mo
re
6.If
Lin
da c
an i
nve
st t
he
mon
ey f
or
10 y
ears
on
ly,w
hic
h a
ccou
nt
wou
ld
give
her
th
e h
igh
er r
etu
rn o
n h
erin
vest
men
t? H
ow m
uch
mor
e m
oney
wou
ld s
he
mak
e by
ch
oosi
ng
the
hig
her
payi
ng
acco
un
t?A
cco
un
t A
;sh
e’ll
mak
e $2
8098
.95
�$2
8000
�$9
8.95
mo
re
7.If
Lin
da c
an i
nve
st t
he
mon
ey f
or
20 y
ears
on
ly,w
hic
h a
ccou
nt
wou
ld
give
her
th
e h
igh
er r
etu
rn o
n h
erin
vest
men
t? H
ow m
uch
mor
e m
oney
wou
ld s
he
mak
e by
ch
oosi
ng
the
hig
her
payi
ng
acco
un
t?A
cco
un
t A
;sh
e’ll
mak
e $3
9477
.55
�$3
6000
�$3
477.
55m
ore
9-5
Cha
pter
938
Gle
ncoe
Alg
ebra
2
Use
a c
alcu
lato
r to
eva
luat
e ea
ch e
xpre
ssio
n t
o fo
ur
dec
imal
pla
ces.
1.e1
.54.
4817
2.ln
82.
0794
3.ln
3.2
1.16
324.
e�0.
60.
5488
5.e4
.266
.686
36.
ln 1
07.
e�2.
50.
0821
8.ln
0.0
37�
3.29
68
Wri
te a
n e
qu
ival
ent
exp
onen
tial
or
loga
rith
mic
eq
uat
ion
.
9.ln
50
�x
10.l
n 3
6 �
2x11
.ln
6
1.79
1812
.ln
9.3
2.
2300
ex
�50
e2x
�36
e1.7
918
6
e2.
2300
9.
3
13.e
x�
814
.e5
�10
x15
.e�
x�
416
.e2
�x
�1
x�
ln 8
5 �
ln 1
0xx
��
ln 4
2 �
ln (
x�
1)
Eva
luat
e ea
ch e
xpre
ssio
n.
17.e
ln 1
212
18.e
ln 3
x3x
19.l
n e
�1
�1
20.l
n e
�2y
�2y
Sol
ve e
ach
eq
uat
ion
or
ineq
ual
ity.
21.e
x�
922
.e�
x�
3123
.ex
�1.
124
.ex
�5.
8
{x|x
�2.
1972
}�
3.43
400.
0953
1.75
79
25.2
ex�
3 �
126
.5ex
�1
�7
27.4
�ex
�19
28.�
3ex
�10
�8
0.69
31{x
|x
0.18
23}
2.70
81{x
|x�
�0.
4055
}
29.e
3x�
830
.e�
4x�
531
.e0.
5x�
632
.2e5
x�
24
0.69
31�
0.40
243.
5835
0.49
70
33.e
2x�
1 �
5534
.e3x
�5
�32
35.9
�e2
x�
1036
.e�
3x�
7 �
15
1.99
451.
2036
0{x
|x�
�0.
6931
}
37.l
n 4
x�
338
.ln
(�
2x)
�7
39.l
n 2
.5x
�10
40.l
n (
x�
6) �
1
5.02
14�
548.
3166
8810
.586
38.
7183
41.l
n (
x�
2) �
342
.ln
(x
�3)
�5
43.l
n 3
x�
ln 2
x�
944
.ln
5x
�ln
x�
7
18.0
855
145.
4132
36.7
493
14.8
097
INV
ESTI
NG
For
Exe
rcis
es 4
5 an
d 4
6,u
se t
he
form
ula
for
con
tin
uou
sly
com
pou
nd
ed i
nte
rest
,A�
Per
t ,w
her
e P
is t
he
pri
nci
pal
,ris
th
e an
nu
al i
nte
rest
rate
,an
d t
is t
he
tim
e in
yea
rs.
45.I
f S
arit
a de
posi
ts $
1000
in
an
acc
oun
t pa
yin
g 3.
4% a
nn
ual
in
tere
st c
ompo
un
ded
con
tin
uou
sly,
wh
at i
s th
e ba
lan
ce i
n t
he
acco
un
t af
ter
5 ye
ars?
$118
5.30
46.H
ow l
ong
wil
l it
tak
e th
e ba
lan
ce i
n S
arit
a’s
acco
un
t to
rea
ch $
2000
?ab
ou
t 20
.4 y
r
47.R
AD
IOA
CTI
VE
DEC
AY
Th
e am
oun
t of
a r
adio
acti
ve s
ubs
tan
ce y
that
rem
ain
s af
ter
tye
ars
is g
iven
by
the
equ
atio
n y
�ae
kt,w
her
e a
is t
he
init
ial
amou
nt
pres
ent
and
kis
the
deca
y co
nst
ant
for
the
radi
oact
ive
subs
tan
ce.I
f a
�10
0,y
�50
,an
d k
��
0.03
5,fi
nd
t.ab
ou
t 19
.8 y
r
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
9-5
Prac
tice
Bas
e e
and
Nat
ura
l Lo
gar
ith
ms
Chapter 9 A19 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lessons 9-5 and 9-6)
9-6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
941
Gle
ncoe
Alg
ebra
2
Lesson 9-6
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 9
-6 i
n y
our
text
boo
k.
•B
etw
een
wh
ich
tw
o ye
ars
show
n i
n t
he
tabl
e di
d th
e ca
r de
prec
iate
by
the
grea
test
amou
nt?
bet
wee
n y
ears
0 a
nd
1•
Des
crib
e tw
o w
ays
to c
alcu
late
th
e va
lue
of t
he
car
6 ye
ars
afte
r it
was
pu
rch
ased
.(D
o n
ot a
ctu
ally
cal
cula
te t
he
valu
e.)
Sam
ple
an
swer
:1.
Mu
ltip
ly $
9200
.66
by0.
16 a
nd
su
btr
act
the
resu
lt f
rom
$92
00.6
6.2.
Mu
ltip
ly $
9200
.66
by 0
.84.
Rea
d t
he
Less
on
1.S
tate
wh
eth
er e
ach
sit
uat
ion
is
an e
xam
ple
of e
xpon
enti
al g
row
thor
dec
ay.
a.A
cit
y h
ad 4
2,00
0 re
side
nts
in
198
0 an
d 12
8,00
0 re
side
nts
in
200
0.g
row
th
b.
Rau
l co
mpa
red
the
valu
e of
his
car
wh
en h
e bo
ugh
t it
new
to
the
valu
e w
hen
he
trad
ed i
t in
six
yea
rs l
ater
.d
ecay
c.A
pal
eon
tolo
gist
com
pare
d th
e am
oun
t of
car
bon
-14
in t
he
skel
eton
of
an a
nim
alw
hen
it
died
to
the
amou
nt
300
year
s la
ter.
dec
ay
d.
Mar
ia d
epos
ited
$75
0 in
a s
avin
gs a
ccou
nt
payi
ng
4.5%
an
nu
al i
nte
rest
com
pou
nde
dqu
arte
rly.
Sh
e di
d n
ot m
ake
any
wit
hdr
awal
s or
fu
rth
er d
epos
its.
Sh
e co
mpa
red
the
bala
nce
in
her
pas
sboo
k im
med
iate
ly a
fter
sh
e op
ened
th
e ac
cou
nt
to t
he
bala
nce
3
year
s la
ter.
gro
wth
2.S
tate
wh
eth
er e
ach
equ
atio
n r
epre
sen
ts e
xpon
enti
al g
row
th o
r de
cay.
a.y
�5e
0.15
tg
row
thb
.y�
1000
(1 �
0.05
)td
ecay
c.y
�0.
3e�
1200
td
ecay
d.y
�2(
1 �
0.00
01)t
gro
wth
Rem
emb
er W
hat
Yo
u L
earn
ed
3.V
isu
aliz
ing
thei
r gr
aph
s is
oft
en a
goo
d w
ay t
o re
mem
ber
the
diff
eren
ce b
etw
een
mat
hem
atic
al e
quat
ions
.How
can
you
r kn
owle
dge
of t
he g
raph
s of
exp
onen
tial
equ
atio
nsfr
om L
esso
n 9
-1 h
elp
you
to
rem
embe
r th
at e
quat
ion
s of
th
e fo
rm y
�a(
1 �
r)t
repr
esen
tex
pon
enti
al g
row
th,w
hil
e eq
uat
ion
s of
th
e fo
rm y
�a(
1 �
r)t
repr
esen
tex
pon
enti
al d
ecay
?S
amp
le a
nsw
er:
If a
�0,
the
gra
ph
of
y�
abx
is a
lway
s in
crea
sin
g if
b
�1
and
is a
lway
s d
ecre
asin
g if
0 �
b�
1.S
ince
ris
alw
ays
a p
osi
tive
nu
mb
er,i
f b
�1
�r,
the
bas
e w
ill b
e g
reat
er t
han
1 a
nd
th
e fu
nct
ion
will
be
incr
easi
ng
(g
row
th),
wh
ile if
b�
1 �
r,th
e b
ase
will
be
less
th
an 1
and
th
e fu
nct
ion
will
be
dec
reas
ing
(d
ecay
).
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Exp
on
enti
al G
row
th a
nd
Dec
ay
9-5
Cha
pter
940
Gle
ncoe
Alg
ebra
2
Ap
pro
xim
atio
ns
for
�an
d e
Th
e fo
llow
ing
expr
essi
on c
an b
e u
sed
to a
ppro
xim
ate
e.If
gre
ater
an
d gr
eate
rva
lues
of
nar
e u
sed,
the
valu
e of
th
e ex
pres
sion
app
roxi
mat
es e
mor
e an
dm
ore
clos
ely.
�1 �
� n1 � �n
An
oth
er w
ay t
o ap
prox
imat
e e
is t
o u
se t
his
in
fin
ite
sum
.Th
e gr
eate
r th
eva
lue
of n
,th
e cl
oser
th
e ap
prox
imat
ion
.
e�
1 �
1 �
�1 2��
� 21 �
3��
� 2�
1 3�
4�
�…
�� 2
�3
�41
�…
�n
��
…
In a
sim
ilar
man
ner
,ca
n b
e ap
prox
imat
ed u
sin
g an
in
fin
ite
prod
uct
disc
over
ed b
y th
e E
ngl
ish
mat
hem
atic
ian
Joh
n W
alli
s (1
616–
1703
).
� 2��
�2 1��
�2 3��
�4 3��
�4 5��
�6 5��
�6 7��
… �
� 2n2 �n
1�
� � 2n
2 �n1
�…
Sol
ve e
ach
pro
ble
m.
1.U
se a
cal
cula
tor
wit
h a
n e
xke
y to
fin
d e
to 7
dec
imal
pla
ces.
2.71
8281
8
2.U
se t
he
expr
essi
on �1
�� n1 � �n
to a
ppro
xim
ate
eto
3 d
ecim
al p
lace
s.U
se
5,10
0,50
0,an
d 70
00 a
s va
lues
of
n.
2.48
8,2.
705,
2.71
6,2.
718
3.U
se t
he
infi
nit
e su
m t
o ap
prox
imat
e e
to 3
dec
imal
pla
ces.
Use
th
e w
hol
e n
um
bers
fro
m 3
th
rou
gh 6
as
valu
es o
f n
.2.
667,
2.70
8,2.
717,
2.71
8
4.W
hic
h a
ppro
xim
atio
n m
eth
od a
ppro
ach
es t
he
valu
e of
em
ore
quic
kly?
the
infi
nit
e su
m5.
Use
a c
alcu
lato
r w
ith
a
key
to fi
nd
to
7 d
ecim
al p
lace
s.3.
1415
927
6.U
se t
he
infi
nit
e pr
odu
ct t
o ap
prox
imat
e
to 3
dec
imal
pla
ces.
Use
th
e w
hol
e n
um
bers
fro
m 3
th
rou
gh 6
as
valu
es o
f n
.2.
926,
2.97
2,3.
002,
3.02
3
7.D
oes
the
infi
nit
e pr
odu
ct g
ive
good
app
roxi
mat
ion
s fo
r
quic
kly?
no
8.S
how
th
at
4�
5
is e
qual
to
e6to
4 d
ecim
al p
lace
s.To
4 d
ecim
al p
lace
s,th
ey b
oth
eq
ual
403
.428
8.9.
Wh
ich
is
larg
er,e
or
e ?
e�>
�e
10.T
he
expr
essi
on x
reac
hes
a m
axim
um
val
ue
at x
�e.
Use
th
is f
act
to
prov
e th
e in
equ
alit
y yo
u f
oun
d in
Exe
rcis
e 9.
e�1 e�>
�� �1 � ;
� e�1 e� ��
e>
� �� �1 � ��
e ;e�
> �
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
9-5
Enri
chm
ent
Chapter 9 A20 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-6)
9-6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
943
Gle
ncoe
Alg
ebra
2
Lesson 9-6
Exp
on
enti
al G
row
thP
opu
lati
on i
ncr
ease
an
d gr
owth
of
bact
eria
col
onie
s ar
e ex
ampl
esof
exp
onen
tial
gro
wth
.Wh
en a
qu
anti
ty i
ncr
ease
s by
a f
ixed
per
cen
t ea
ch t
ime
peri
od,t
he
amou
nt
of t
hat
qu
anti
ty a
fter
tti
me
peri
ods
is g
iven
by
y�
a(1
�r)
t ,w
her
e a
is t
he
init
ial
amou
nt
and
ris
th
e pe
rcen
t in
crea
se (
or r
ate
of g
row
th)
expr
esse
d as
a d
ecim
al.
An
oth
er e
xpon
enti
al g
row
th m
odel
oft
en u
sed
by s
cien
tist
s is
y�
aekt
,wh
ere
kis
a c
onst
ant.
A c
omp
ute
r en
gin
eer
is h
ired
for
a s
alar
y of
$28
,000
.If
she
gets
a5%
rai
se e
ach
yea
r,af
ter
how
man
y ye
ars
wil
l sh
e b
e m
akin
g $5
0,00
0 or
mor
e?U
se t
he
expo
nen
tial
gro
wth
mod
el w
ith
a�
28,0
00,y
�50
,000
,an
d r
�0.
05 a
nd
solv
e fo
r t.
y�
a(1
�r)
tE
xpon
entia
l gro
wth
form
ula
50,0
00 �
28,0
00(1
�0.
05)t
y�
50,0
00,
a�
28,0
00,
r�
0.05
�(1
.05)
tD
ivid
e ea
ch s
ide
by 2
8,00
0.
log
���
log
(1.0
5)t
Pro
pert
y of
Equ
ality
of
Loga
rithm
s
log
���
tlo
g 1.
05P
ower
Pro
pert
y
t�
Div
ide
each
sid
e by
log
1.05
.
t
11.9
yea
rsU
se a
cal
cula
tor.
If r
aise
s ar
e gi
ven
an
nu
ally
,sh
e w
ill
be m
akin
g ov
er $
50,0
00 i
n 1
2 ye
ars.
1.B
AC
TER
IA G
RO
WTH
A c
erta
in s
trai
n o
f ba
cter
ia g
row
s fr
om 4
0 to
326
in
120
min
ute
s.F
ind
kfo
r th
e gr
owth
for
mu
la y
�ae
kt,w
her
e t
is i
n m
inu
tes.
abo
ut
0.01
75
2.IN
VES
TMEN
TC
arl
plan
s to
in
vest
$50
0 at
8.2
5% i
nte
rest
,com
pou
nde
d co
nti
nu
ousl
y.H
ow l
ong
wil
l it
tak
e fo
r h
is m
oney
to
trip
le?
abo
ut
14 y
ears
3.SC
HO
OL
POPU
LATI
ON
Th
ere
are
curr
entl
y 85
0 st
ude
nts
at
the
hig
h s
choo
l,w
hic
hre
pres
ents
fu
ll c
apac
ity.
Th
e to
wn
pla
ns
an a
ddit
ion
to
hou
se 4
00 m
ore
stu
den
ts.I
f th
e sc
hoo
l po
pula
tion
gro
ws
at 7
.8%
per
yea
r,in
how
man
y ye
ars
wil
l th
e n
ew a
ddit
ion
be f
ull
?ab
ou
t 5
year
s
4.EX
ERC
ISE
Hu
go b
egin
s a
wal
kin
g pr
ogra
m b
y w
alki
ng
mil
e pe
r da
y fo
r on
e w
eek.
Eac
h w
eek
ther
eaft
er h
e in
crea
ses
his
mil
eage
by
10%
.Aft
er h
ow m
any
wee
ks i
s h
ew
alki
ng
mor
e th
an 5
mil
es p
er d
ay?
24 w
eeks
5.V
OC
AB
ULA
RY G
RO
WTH
Wh
en E
mil
y w
as 1
8 m
onth
s ol
d,sh
e h
ad a
10-
wor
dvo
cabu
lary
.By
the
tim
e sh
e w
as 5
yea
rs o
ld (
60 m
onth
s),h
er v
ocab
ular
y w
as 2
500
wor
ds.
If h
er v
ocab
ular
y in
crea
sed
at a
con
stan
t pe
rcen
t pe
r m
onth
,wha
t w
as t
hat
incr
ease
?ab
ou
t 14
%
1 � 2
log
��5 20 8��
� log
1.05
50 � 2850 � 2850 � 28
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(con
tinued
)
Exp
on
enti
al G
row
th a
nd
Dec
ay
Exer
cise
s
Exam
ple
9-6
Cha
pter
942
Gle
ncoe
Alg
ebra
2
Exp
on
enti
al D
ecay
Dep
reci
atio
n o
f va
lue
and
radi
oact
ive
deca
y ar
e ex
ampl
es o
fex
pon
enti
al d
ecay
.Wh
en a
qu
anti
ty d
ecre
ases
by
a fi
xed
perc
ent
each
tim
e pe
riod
,th
eam
oun
t of
th
e qu
anti
ty a
fter
tti
me
peri
ods
is g
iven
by
y�
a(1
�r)
t ,w
her
e a
is t
he
init
ial
amou
nt
and
ris
th
e pe
rcen
t de
crea
se e
xpre
ssed
as
a de
cim
al.
An
oth
er e
xpon
enti
al d
ecay
mod
el o
ften
use
d by
sci
enti
sts
is y
�ae
�kt
,wh
ere
kis
a c
onst
ant.
CO
NSU
MER
PR
ICES
As
tech
nol
ogy
adva
nce
s,th
e p
rice
of
man
yte
chn
olog
ical
dev
ices
su
ch a
s sc
ien
tifi
c ca
lcu
lato
rs a
nd
cam
cord
ers
goes
dow
n.
On
e b
ran
d o
f h
and
-hel
d o
rgan
izer
sel
ls f
or $
89.
a.If
its
pri
ce d
ecre
ases
by
6% p
er y
ear,
how
mu
ch w
ill
it c
ost
afte
r 5
year
s?U
se t
he
expo
nen
tial
dec
ay m
odel
wit
h i
nit
ial
amou
nt
$89,
perc
ent
decr
ease
0.0
6,an
dti
me
5 ye
ars.
y�
a(1
�r)
tE
xpon
entia
l dec
ay fo
rmul
a
y�
89(1
�0.
06)5
a�
89,
r�
0.06
, t
�5
y�
$65.
32A
fter
5 y
ears
th
e pr
ice
wil
l be
$65
.32.
b.
Aft
er h
ow m
any
year
s w
ill
its
pri
ce b
e $5
0?To
fin
d w
hen
the
pric
e w
ill b
e $5
0,ag
ain
use
the
expo
nent
ial d
ecay
for
mul
a an
d so
lve
for
t.y
�a(
1 �
r)t
Exp
onen
tial d
ecay
form
ula
50 �
89(1
�0.
06)t
y�
50,
a�
89,
r�
0.06
�(0
.94)
tD
ivid
e ea
ch s
ide
by 8
9.
log
���
log
(0.9
4)t
Pro
pert
y of
Equ
ality
for
Loga
rithm
s
log
���
tlo
g 0.
94P
ower
Pro
pert
y
t�
Div
ide
each
sid
e by
log
0.94
.
t
9.3
Th
e pr
ice
wil
l be
$50
aft
er a
bou
t 9.
3 ye
ars.
1.B
USI
NES
SA
fu
rnit
ure
sto
re i
s cl
osin
g ou
t it
s bu
sin
ess.
Eac
h w
eek
the
own
er l
ower
spr
ices
by
25%
.Aft
er h
ow m
any
wee
ks w
ill
the
sale
pri
ce o
f a
$500
ite
m d
rop
belo
w $
100?
6 w
eeks
CA
RB
ON
DA
TIN
GU
se t
he
form
ula
y�
ae�
0.00
012t
,wh
ere
ais
th
e in
itia
l am
oun
t of
Car
bon
-14,
tis
th
e n
um
ber
of
year
s ag
o th
e an
imal
liv
ed,a
nd
yis
th
e re
mai
nin
gam
oun
t af
ter
tye
ars.
2.H
ow o
ld is
a f
ossi
l rem
ain
that
has
lost
95%
of
its
Car
bon-
14?
abo
ut
25,0
00 y
ears
old
3.H
ow o
ld is
a s
kele
ton
that
has
95%
of
its
Car
bon-
14 r
emai
ning
?ab
ou
t 42
7.5
year
s o
ld
log
��5 80 9��
��
log
0.94
50 � 8950 � 8950 � 89NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
9-6
Exer
cise
s
Exam
ple
Stud
y G
uide
and
Inte
rven
tion
Exp
on
enti
al G
row
th a
nd
Dec
ay
Chapter 9 A21 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-6)
9-6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
945
Gle
ncoe
Alg
ebra
2
Lesson 9-6
1.IN
VES
TIN
GT
he f
orm
ula
A�
P�1
��2t
give
s th
e va
lue
of a
n in
vest
men
t af
ter
tye
ars
in
an a
ccou
nt
that
ear
ns
an a
nn
ual
in
tere
st r
ate
rco
mpo
un
ded
twic
e a
year
.Su
ppos
e $5
00is
in
vest
ed a
t 6%
an
nu
al i
nte
rest
com
pou
nde
d tw
ice
a ye
ar.I
n h
ow m
any
year
s w
ill
the
inve
stm
ent
be w
orth
$10
00?
abo
ut
11.7
yr
2.B
AC
TER
IAH
ow m
any
hou
rs w
ill
it t
ake
a cu
ltu
re o
f ba
cter
ia t
o in
crea
se f
rom
20
to20
00 i
f th
e gr
owth
rat
e pe
r h
our
is 8
5%?
abo
ut
7.5
h
3.R
AD
IOA
CTI
VE
DEC
AY
A r
adio
acti
ve s
ubs
tan
ce h
as a
hal
f-li
fe o
f 32
yea
rs.F
ind
the
con
stan
t k
in t
he
deca
y fo
rmu
la f
or t
he
subs
tan
ce.
abo
ut
0.02
166
4.D
EPR
ECIA
TIO
NA
pie
ce o
f m
ach
iner
y va
lued
at
$250
,000
dep
reci
ates
at
a fi
xed
rate
of
12%
per
yea
r.A
fter
how
man
y ye
ars
wil
l th
e va
lue
hav
e de
prec
iate
d to
$10
0,00
0?ab
ou
t 7.
2 yr
5.IN
FLA
TIO
NFo
r D
ave
to b
uy a
new
car
com
para
bly
equi
pped
to
the
one
he b
ough
t 8
year
sag
o w
ould
cos
t $1
2,50
0.S
ince
Dav
e bo
ugh
t th
e ca
r,th
e in
flat
ion
rat
e fo
r ca
rs l
ike
his
has
been
at
an a
vera
ge a
nn
ual
rat
e of
5.1
%.I
f D
ave
orig
inal
ly p
aid
$840
0 fo
r th
e ca
r,h
owlo
ng
ago
did
he
buy
it?
abo
ut
8 yr
6.R
AD
IOA
CTI
VE
DEC
AY
Cob
alt,
an e
lem
ent
use
d to
mak
e al
loys
,has
sev
eral
iso
tope
s.O
ne
of t
hes
e,co
balt
-60,
is r
adio
acti
ve a
nd
has
a h
alf-
life
of
5.7
year
s.C
obal
t-60
is
use
d to
trac
e th
e pa
th o
f n
onra
dioa
ctiv
e su
bsta
nce
s in
a s
yste
m.W
hat
is
the
valu
e of
kfo
rC
obal
t-60
?ab
ou
t 0.
1216
7.W
HA
LES
Mod
ern
wh
ales
app
eare
d 5�
10 m
illi
on y
ears
ago
.Th
e ve
rteb
rae
of a
wh
ale
disc
over
ed b
y pa
leon
tolo
gist
s co
nta
in r
ough
ly 0
.25%
as
mu
ch c
arbo
n-1
4 as
th
ey w
ould
hav
e co
nta
ined
wh
en t
he
wh
ale
was
ali
ve.H
ow l
ong
ago
did
the
wh
ale
die?
Use
k
�0.
0001
2.ab
ou
t 50
,000
yr
8.PO
PULA
TIO
NT
he
popu
lati
on o
f ra
bbit
s in
an
are
a is
mod
eled
by
the
grow
th e
quat
ion
P(t
) �
8e0.
26t ,
wh
ere
Pis
in
th
ousa
nds
an
d t
is i
n y
ears
.How
lon
g w
ill
it t
ake
for
the
popu
lati
on t
o re
ach
25,
000?
abo
ut
4.4
yr
9.D
EPR
ECIA
TIO
NA
com
pute
r sy
stem
dep
reci
ates
at
an a
vera
ge r
ate
of 4
% p
er m
onth
.If
the
valu
e of
th
e co
mpu
ter
syst
em w
as o
rigi
nal
ly $
12,0
00,i
n h
ow m
any
mon
ths
is i
tw
orth
$73
50?
abo
ut
12 m
o
10.B
IOLO
GY
In a
lab
orat
ory,
a cu
ltu
re i
ncr
ease
s fr
om 3
0 to
195
org
anis
ms
in 5
hou
rs.
Wh
at i
s th
e h
ourl
y gr
owth
rat
e in
th
e gr
owth
for
mu
la y
�a
(1 �
r)t ?
abo
ut
45.4
%
r � 2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Exp
on
enti
al G
row
th a
nd
Dec
ay
9-6
Cha
pter
944
Gle
ncoe
Alg
ebra
2
1.FI
SHIN
GIn
an
ove
r-fi
shed
are
a,th
e ca
tch
of
a ce
rtai
n f
ish
is
decr
easi
ng
at a
n a
vera
gera
te o
f 8%
per
yea
r.If
th
is d
ecli
ne
pers
ists
,how
lon
g w
ill
it t
ake
for
the
catc
h t
o re
ach
hal
f of
th
e am
oun
t be
fore
th
e de
clin
e?ab
ou
t 8.
3 yr
2.IN
VES
TIN
GA
lex
inve
sts
$200
0 in
an
acc
oun
t th
at h
as a
6%
an
nu
al r
ate
of g
row
th.T
oth
e n
eare
st y
ear,
wh
en w
ill
the
inve
stm
ent
be w
orth
$36
00?
10 y
r
3.PO
PULA
TIO
NA
cu
rren
t ce
nsu
s sh
ows
that
th
e po
pula
tion
of
a ci
ty i
s 3.
5 m
illi
on.U
sin
gth
e fo
rmu
la P
�ae
rt,f
ind
the
expe
cted
pop
ula
tion
of
the
city
in
30
year
s if
th
e gr
owth
rate
rof
th
e po
pula
tion
is
1.5%
per
yea
r,a
repr
esen
ts t
he
curr
ent
popu
lati
on i
n m
illi
ons,
and
tre
pres
ents
th
e ti
me
in y
ears
.ab
ou
t 5.
5 m
illio
n
4.PO
PULA
TIO
NT
he
popu
lati
on P
in t
hou
san
ds o
f a
city
can
be
mod
eled
by
the
equ
atio
nP
�80
e0.0
15t ,
wh
ere
tis
th
e ti
me
in y
ears
.In
how
man
y ye
ars
wil
l th
e po
pula
tion
of
the
city
be
120,
000?
abo
ut
27 y
r
5.B
AC
TER
IAH
ow m
any
days
wil
l it
tak
e a
cult
ure
of
bact
eria
to
incr
ease
fro
m 2
000
to50
,000
if
the
grow
th r
ate
per
day
is 9
3.2%
?ab
ou
t 4.
9 d
ays
6.N
UC
LEA
R P
OW
ERT
he
elem
ent
plu
ton
ium
-239
is
hig
hly
rad
ioac
tive
.Nu
clea
r re
acto
rsca
n p
rodu
ce a
nd
also
use
th
is e
lem
ent.
Th
e h
eat
that
plu
ton
ium
-239
em
its
has
hel
ped
topo
wer
equ
ipm
ent
on t
he
moo
n.I
f th
e h
alf-
life
of
plu
ton
ium
-239
is
24,3
60 y
ears
,wh
at i
sth
e va
lue
of k
for
this
ele
men
t?ab
ou
t 0.
0000
2845
7.D
EPR
ECIA
TIO
NA
Glo
bal
Pos
itio
nin
g S
atel
lite
(G
PS
) sy
stem
use
s sa
tell
ite
info
rmat
ion
to l
ocat
e gr
oun
d po
siti
on.A
bu’s
su
rvey
ing
firm
bou
ght
a G
PS
sys
tem
for
$12
,500
.Th
eG
PS
dep
reci
ated
by
a fi
xed
rate
of
6% a
nd
is n
ow w
orth
$86
00.H
ow l
ong
ago
did
Abu
buy
the
GP
S s
yste
m?
abo
ut
6.0
yr
8.B
IOLO
GY
In a
lab
orat
ory,
an o
rgan
ism
gro
ws
from
100
to
250
in 8
hou
rs.W
hat
is
the
hou
rly
grow
th r
ate
in t
he
grow
th f
orm
ula
y�
a(1
�r)
t ?ab
ou
t 12
.13%
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
9-6
Skill
s Pr
acti
ceE
xpo
nen
tial
Gro
wth
an
d D
ecay
Chapter 9 A22 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 9-6)
9-6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Cha
pter
947
Gle
ncoe
Alg
ebra
2
Lesson 9-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Eff
ecti
ve A
nn
ual
Yie
ldW
hen
in
tere
st i
s co
mpo
un
ded
mor
e th
an o
nce
per
yea
r,th
e ef
fect
ive
ann
ual
yiel
d is
hig
her
th
an t
he
ann
ual
in
tere
st r
ate.
Th
e ef
fect
ive
ann
ual
yie
ld,E
,is
the
inte
rest
rat
e th
at w
ould
giv
e th
e sa
me
amou
nt
of i
nte
rest
if
the
inte
rest
wer
e co
mpo
un
ded
once
per
yea
r.If
Pdo
llar
s ar
e in
vest
ed f
or o
ne
year
,th
eva
lue
of t
he
inve
stm
ent
at t
he
end
of t
he
year
is
A�
P(1
�E
).If
Pdo
llar
sar
e in
vest
ed f
or o
ne
year
at
a n
omin
al r
ate
rco
mpo
un
ded
nti
mes
per
yea
r,
the
valu
e of
th
e in
vest
men
t at
th
e en
d of
th
e ye
ar i
s A
�P�1
�� nr � �n
.Set
tin
g
the
amou
nts
equ
al a
nd
solv
ing
for
Ew
ill
prod
uce
a f
orm
ula
for
th
e ef
fect
ive
ann
ual
yie
ld.
P(1
�E
) �
P�1
�� nr � �n
1 �
E�
�1 �
� nr � �n
E�
�1 �
� nr � �n�
1
If c
ompo
un
din
g is
con
tin
uou
s,th
e va
lue
of t
he
inve
stm
ent
at t
he
end
of o
ne
year
is
A�
Per
.Aga
in s
et t
he
amou
nts
equ
al a
nd
solv
e fo
r E
.A f
orm
ula
for
the
effe
ctiv
e an
nu
al y
ield
un
der
con
tin
uou
s co
mpo
un
din
g is
obt
ain
ed.
P(1
�E
) �
Per
1 �
E�
er
E�
er�
1
Enri
chm
ent
Fin
d t
he
effe
ctiv
ean
nu
al y
ield
of
an i
nve
stm
ent
mad
e at
7.5%
com
pou
nd
ed m
onth
ly.
r�
0.07
5
n�
12
E�
�1 �
�0.10 275 �
�12�
1 �
7.7
6%
Fin
d t
he
effe
ctiv
ean
nu
al y
ield
of
an i
nve
stm
ent
mad
e at
6.25
% c
omp
oun
ded
con
tin
uou
sly.
r�
0.06
25
E�
e0.0
625
�1
� 6
.45%
Fin
d t
he
effe
ctiv
e an
nu
al y
ield
for
eac
h i
nve
stm
ent.
1.10
% c
ompo
un
ded
quar
terl
y10
.38%
2.8.
5% c
ompo
un
ded
mon
thly
8.84
%
3.9.
25%
com
pou
nde
d co
nti
nu
ousl
y9.
69%
4.7.
75%
com
pou
nde
d co
nti
nu
ousl
y8.
06%
5.6.
5% c
ompo
un
ded
dail
y (a
ssu
me
a 36
5-da
y ye
ar)
6.72
%
6.W
hic
h i
nve
stm
ent
yiel
ds m
ore
inte
rest
—9%
com
pou
nde
d co
nti
nu
ousl
y or
9.
2% c
ompo
un
ded
quar
terl
y?9.
2% q
uar
terl
y
Exam
ple
1Ex
amp
le 2
Exer
cise
s
9-6
Cha
pter
946
Gle
ncoe
Alg
ebra
2
Wor
d Pr
oble
m P
ract
ice
Exp
on
enti
al G
row
th a
nd
Dec
ay
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.PR
OG
RA
MM
ING
For
rea
son
s h
avin
g to
do
wit
h s
peed
,a c
ompu
ter
prog
ram
mer
wis
hes
to
mod
el p
opu
lati
onsi
ze u
sin
g a
nat
ura
l ba
se e
xpon
enti
alfu
nct
ion
.How
ever
,th
e pr
ogra
mm
er
is t
old
that
th
e u
sers
of
the
prog
ram
w
ill
be t
hin
kin
g in
ter
ms
of t
he
ann
ual
perc
enta
ge i
ncr
ease
.Let
rbe
th
epe
rcen
tage
th
at t
he
popu
lati
on i
ncr
ease
sea
ch y
ear.
Fin
d th
e va
lue
for
kin
ter
ms
of r
so t
hat
ek�
1 �
r.k
�ln
(1 �
r)
2.C
AR
BO
N D
ATI
NG
Arc
heo
logi
sts
un
cove
r an
an
cien
t w
oode
n t
ool.
Th
eyan
alyz
e th
e to
ol a
nd
fin
d th
at i
t h
as
22%
as
mu
ch c
arbo
n–1
4 co
mpa
red
to
the
like
ly a
mou
nt
that
it
con
tain
edw
hen
it
was
mad
e.G
iven
th
at t
he
hal
f-li
fe o
f ca
rbon
–14
is a
bou
t 57
30 y
ears
,ab
out
how
old
is
the
arti
fact
? R
oun
dyo
ur
answ
er t
o th
e n
eare
st 1
00 y
ears
.12
,500
yea
rs
3.PO
PULA
TIO
NT
he
dou
blin
g ti
me
of
a po
pula
tion
is
dye
ars.
Th
e po
pula
tion
size
can
be
mod
eled
by
an e
xpon
enti
aleq
uat
ion
of
the
form
Pek
t ,w
her
e P
is
the
init
ial
popu
lati
on s
ize
and
tis
tim
e.W
hat
is
kin
ter
ms
of d
?
k �
ln 2
4.PO
PULA
TIO
NL
ouis
a re
ad t
hat
th
epo
pula
tion
of
her
tow
n h
as i
ncr
ease
dst
eadi
ly a
t a
rate
of
2% e
ach
yea
r.T
oday
,th
e po
pula
tion
of
her
tow
n h
as g
row
n
to 6
8,73
5.B
ased
on
th
is i
nfo
rmat
ion
,w
hat
was
th
e po
pula
tion
of
her
tow
n
100
year
s ag
o?A
bo
ut
9,48
8 p
eop
le.
1 � d
CO
NSU
MER
AW
AR
ENES
SF
or E
xerc
ises
5–7,
use
th
e fo
llow
ing
info
rmat
ion
.
Jaso
n w
ants
to
buy
a br
and
new
hig
h-
defi
nit
ion
(H
D)
tele
visi
on.H
e co
uld
bu
y on
e n
ow b
ecau
se h
e h
as $
7000
to
spen
d,bu
t h
e th
inks
th
at i
f h
e w
aits
,th
e qu
alit
y of
HD
tel
evis
ion
s w
ill
impr
ove.
His
$70
00ea
rns
2.5%
in
tere
st a
nn
ual
ly c
ompo
un
ded
con
tin
uou
sly.
Th
e te
levi
sion
he
wan
ts t
o bu
yco
sts
$500
0 n
ow,b
ut
the
cost
in
crea
ses
each
year
by
7%.
5.W
rite
a n
atu
ral
base
exp
onen
tial
fun
ctio
n t
hat
giv
es t
he
valu
e of
Jas
on’s
acco
un
t as
a f
un
ctio
n o
f ti
me
t.70
00e
0.02
5t
6.W
rite
a n
atu
ral
base
exp
onen
tial
fun
ctio
n t
hat
giv
es t
he
cost
of
the
tele
visi
on J
ason
wan
ts a
s a
fun
ctio
n
of t
ime
t.50
00e
(ln
1.0
7)t
7.In
how
man
y ye
ars
wil
l th
e co
st o
f th
ete
levi
sion
exc
eed
the
valu
e of
th
e m
oney
in J
ason
’s a
ccou
nt?
In
oth
er w
ords
,how
mu
ch t
ime
does
Jas
on h
ave
to d
ecid
ew
het
her
he
wan
ts t
o bu
y th
e te
levi
sion
?R
oun
d yo
ur
answ
er t
o th
e n
eare
st t
enth
of a
yea
r.7.
9 ye
ars
Chapter 9 A23 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 9-6)
9-6
Cha
pter
948
Gle
ncoe
Alg
ebra
2
Spre
adsh
eet
Act
ivit
yN
et P
rese
nt V
alu
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.If
th
e N
PV
is
grea
ter
than
th
e co
st,t
he
inve
stm
ent
wil
l pa
y fo
r it
self
.B
ased
on
th
e sp
read
shee
t sh
own
abo
ve,w
ould
it
be c
ost-
effe
ctiv
e fo
r th
eco
mpa
ny
to b
uy
the
van
? E
xpla
in.
Th
e co
st is
act
ual
ly a
bo
ut
$75
gre
ater
th
an t
he
NP
V,so
it w
ou
ld n
ot
be
cost
-eff
ecti
ve t
o b
uy
the
van
.2.
Fou
r ti
mes
a y
ear,
Jose
y an
d D
rew
pu
blis
h a
mag
azin
e.T
hey
wan
t to
bu
y a
colo
r pr
inte
r th
at c
osts
$17
50.T
he
cost
of
capi
tal
for
this
pu
rch
ase
wou
ldbe
6%
.Th
ey a
re p
lan
nin
g to
rai
se t
he
pric
e of
th
eir
mag
azin
e fr
om $
1 to
$2.C
reat
e a
spre
adsh
eet
to d
eter
min
e th
e N
PV
for
th
is p
urc
has
e.a.
The
last
issu
e of
the
mag
azin
e so
ld 5
00 c
opie
s.If
eac
h is
sue
of t
he m
agaz
ine
prin
ted
in c
olor
sel
ls 1
00 c
opie
s m
ore
than
th
e pr
evio
us
issu
e,is
th
epr
inte
r a
good
in
vest
men
t af
ter
one
year
? E
xpla
in.
No
,aft
er o
ne
year
th
e N
PV
is o
nly
ab
ou
t $1
682.
14.
b.I
f th
e sa
les
of t
he
mag
azin
e co
nti
nu
e to
ris
e at
th
e sa
me
rate
,is
the
prin
ter
a go
od i
nve
stm
ent
afte
r tw
o ye
ars?
Yes,
afte
r tw
o y
ears
th
eN
PV
is a
bo
ut
$521
0.28
.Th
e N
PV
is a
bo
ut
$346
0.28
gre
ater
than
th
e co
st.
3.a.
Cal
cula
te t
he
NP
V f
or a
n i
nve
stm
ent
over
a p
erio
d of
six
yea
rs i
f th
eco
st o
f ca
pita
l is
4.5
% a
nd
the
inve
stm
ent
wil
l br
ing
a ca
sh f
low
of
$750
ever
y ye
ar.
Th
e N
PV
wo
uld
be
abo
ut
$386
8.40
.b
.Wou
ld t
his
be
a go
od i
nve
stm
ent
of $
3000
? E
xpla
in?
Yes,
the
NP
V is
$113
1.60
gre
ater
th
an t
he
cost
.
You
have
lear
ned
how
to
use
expo
nent
ial a
nd lo
gari
thm
ic f
unct
ions
to
perf
orm
a nu
mbe
r of
fin
anci
al a
naly
ses.
Spr
eads
heet
s ca
n be
use
d to
per
form
man
yty
pes
of a
naly
ses,
such
as
calc
ulat
ing
the
Net
Pre
sent
Val
ue o
f ex
pend
itur
esor
in
vest
men
ts.F
or e
xam
ple,
wh
en a
bu
sin
ess
own
er i
s co
nsi
deri
ng
a m
ajor
purc
has
e,it
is
a go
od i
dea
to f
ind
out
wh
eth
er t
he
inve
stm
ent
wil
l be
prof
itab
le i
n t
he
futu
re.C
onsi
der
the
exam
ple
of a
loc
al r
esta
ura
nt-
deli
very
serv
ice
that
is
deba
tin
g w
het
her
to
buy
a u
sed
van
for
$80
00.T
he
own
ers
of t
he
com
pan
y es
tim
ate
that
th
eva
n w
ill
brin
g in
$25
00 p
er y
ear
over
fou
r ye
ars.
Th
ey c
an u
se t
he
foll
owin
g fo
rmu
la t
o fi
nd
the
pres
ent
valu
e of
th
e fu
ture
cas
hfl
ow t
o fi
nd
the
Net
Pre
sen
t V
alu
e(N
PV
),th
at i
s,h
ow m
uch
th
epr
ofit
s w
ould
be
wor
th i
n t
oday
’s
doll
ars.
NP
V�
� (1C �F
n r)n
�,w
her
eC
Fn
�th
e ca
sh
flow
in
per
iod
nan
d r
�th
e co
st o
fca
pita
l,w
hic
h i
s ei
ther
th
e in
tere
stth
at w
ill
be p
aid
on a
loan
or
the
inte
rest
tha
t th
e m
oney
wou
ld e
arn
if it
wer
e in
vest
ed.
NP
V -
Cos
t
$2,2
72.7
3$2
,066
.12
$1,8
78.2
9$1
,707
.53
$7,9
24.6
6
A1 3 4 5 6 7 8 9 10 112
BC
12
1 2 3 4
$2,5
00.0
0$2
,500
.00
$2,5
00.0
0$2
,500
.00
�$7
5.34
Tota
l
Cos
t of C
apita
l (r)
Per
iod
(n)
$8,0
00.0
0C
ost o
f Ass
et
Sh
eet
1S
hee
t 2
Sh
eet
3
0.1
CF
CF
/(1�
R)^ n
Exer
cise
s
