D' Arcy McGee High School May 1st, 2017Duration: 60 minutes

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Major Assignment: Mathematical of Finance Unit

Exponential and Logarithm Functions

#AStUtt.dName: Section: MCU504- 100-

1. Evaluate each expression (12 marks). Round your answer to the nearest tenth. You do not need toshow your work here. Each right answer is worth 2 marks

a) log327 1 c) log164log -b) 636

Answer: 3 Answer: -2 Answer: esd) log327 e) log., 210

logO.044-4 f)

Answer:-11,;)

Answer:3,2- - V·1fAnswer:

2 h) log, V27 2log .-i) log.J2 - -g) ~3 52

-/ Answer: I Answer: - 2~bAnswer:

j)log 1 2.25 k) log345o 1 1) log35.2

-1.5

Answer: -2 Answer: 0 Answer: l·~

CST 11-MATH MCU504: Major Assignment /Math of Finance! Exponential and Logarithm Functions/

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2. Given the exponential equation, 3x = 18. Which of the answers below will solve for x? (2marks)

A. X = log6

B. X = 3log18

~

X _ LOB18)log3

D. X = log 18 - log 3 6

3. Given: 1000 = 7 x 1 which of the answers below will solve for x? (2 marks)

A. log, x=lOOO

B. log, 7 = 1000

'c. log, 1000 = 7

G log71OOO ~

4. A population of insects doubles every 5 days. If there are currently 1200 insects, determine anequation for the population, P, of insects, t: number of days (2 marks)

t

A. P = 1200 (~)5St

B. P = 1200 (~)

c. P = 1200(2)St

cf P = 1200(2)9

CST 11 - MATH MCU504: Major Assignment / Math of Finance! Exponential and Logarithm Functions PageZ

5. The population of a nest of ants can multiply three fold(triple) in 8 weeks. If the population isnow12 000, how many weeks will it take for the population to reach 300000 ants? (2 marks)

(:t- -b'-4t- 4tJ~

lA = /.JOCJD 3) ~ -c_A. 25 weeks c:j /

3D 0 t.? (!M ~ / L ODO l 3) ,8

B.3.1 weeks ,3DOOC:>O~ _ 3, t/&~~- -~ ~-- - -- ~ _/~~Q - t-/ti - -~-----

C. 10.7 weeks ol~ ::::::"5 (t. .2S)e3.4wee9 --T fjg - .&d'~~=t L g -ta-'- :==.23.4sq ..

6. Suppose a certain type of bacteria reproduces according to the equation, B = 100(1.SSY, where xis the time in hours. (10 marks)

(a) At what percentage rate does this type of bacteria reproduce? (2 marks)

1.5";;-= / + 0.51) -7 FrcM7ar rJe z: 55"7

(b) What was the initial number of bacteria? (2 marks)

loO(c) Find the number of bacteria (rounded to the nearest whole number) after:

c.l) 5 hours (Show your work) (2 marks)

Answer: 89/; (o~gq~)

c.2) I day (Show your work) (2 marks)

£) ~ too (;. )))~'f

Answer: ~. t97/147c.3) 3 days (Show your work) (2 marks)

;; 3)(~ ! _\72/j~/[)()Cl 'Jr) z: loo (J.)"'0

_ / If'

Answer: j~00 J( 10

CST 11 - MATH MCU504: Major Assignment / Math of Finance! Exponential_and Logarithm Functions Page 3

7. Josh bought a new car for $24000. Every year it will depreciate in value by 8%. How long will ittake for the car to be worth $16000? (Show you work) (4 marks)

c2tr OM(/- 19.03/- /0 M1)

-7 (!). 92 f ,= /19 d-tJ-rj -? 1.:::24fH

tf fl ~2-L/){t)O- (f). q2-

Answer: /;, 2£r~8. In 2000, the chicken population on a farm was 10,000. The number of chickens increased at a rate

of 9% per year. Predict the population in 2005. (Show you work) (4 marks)

~~~ ~~~?~ IO&tJV(/'D9)r::: IS-3gC~~I~ 0 I

Answer:

9. A laser printer was purchased for $300 in 2001. If its value depreciates at a rate of 30% a year,determine how much it will be worth in 2007. (Show you work) (4 marks) ~/_ o, 30 :::

'J -1- _ /:) 6 ~ 7- 'lDP( =;"-AfJ~u- I r: if,' ~ == "3&0 lO.70 V,70

10. The price of a car that was bought for $20,000 and has depreciated 15% yearly. Find the price ofthe car 6 years later. (Show you work) (4 marks) C-;:=::.l -. i S-1o z: c;> ,is S-

~ f CM' ~ J = &01300 (I'), fY;) c

CST 11 - MATH MCU504: Major Assignment / Math of Finance! Exponential and Logarithm Functions Page 4

11. Find the value of a signed football that was bought for $35 and its value has appreciated 8% eachyear after 20 years later. (Show you work) (4 marks)

'2)f!)

!j: iJ~ 1f6lt~ .' 1:1 = 3~C/. MJ) = 1/'3. /3

-- -----

d./b3 1'3>Answer: r .J

12. A town of7800 grows at a rate of35% every year. Find the size of the city in 10 years. (Show you·work) (4 marks) . /0

~r{id-rcn.(j "7gtJD{ / .3sj

Answer: / S-~g 3/

13. A city of 200,000 is having pollution problems and is decreasing in size 3.5% annually (everyyear). Find the population of this city in 30 years. (Show you work) (4 marks)

-1! rF<~if z; :2M ~ (0.q&:;J"o

Answer:

14. The depreciation of the value for a motorcycle is modeled by y = 10,000(.85) X for x years since2000. In what year was the value of the car was $6,141.25? (Show you work) (4 marks)

»,1,;t;(~ vd».: () z: 10 ()-;;o(D. t,)')~

/1- r;;/1;;' 25 z: / D &1FD (.g c;-)~ --7 ' . iPd(tf'fl:l..r.-:-1qt!ot!J L=]

y-",- - uif (o.g'l)Answer: 200.3

(]~/i)CST 11 - MATH MCU504: Major Assignment / Math of Financel Exponential and Logarithm Functions Page 5

15. A new automobile is purchased for $20,000. If V = JiOOO(0.8)x, is the car's value after x years,about how long will it take for the car to be worth $820? (Show you work) (4 marks)

/V -==~O fJO(D. e) 'I- y-7 g $0 ss= ,;) f) f) 00(0, '3)

_') Y =- uqfg20 -'- Z~oo~LoO- c),. q

Answer: ·/~ c¥-~

16. A bacteria colony started with 2 bacteria. The colony is growing exponentially at 10% per hour.How long will it take to have 300 bacteria? (Show you work) (4 marks)

(t:= J C /, lo)X Y

-y30u ~ d2{/,/O)J S;V =- Cl. 10) X ( )

. I S-o'-7 1==- (~~ - r: It-» (/.I a) Answer: -JJ, (tJ ~11.CS

17. A bacterial culture initially contains 15 bacteria. The number of bacteria increases by 30% every __

twohours, Determine #C/(~/iJi1A)'1J:= /5' (/, ~o)X/ia) The number of bacteria after 8 hours (show your work) (4 marks) X J -h/~ I;' tu[S

C . )%.. !J \Y--7 if::c- Ir J. 3 u ~;7 CJ z: I~ (/, "5D/

()f rz: :fF Jjw()fv.J 'X- t rr-r- (, 3D \ \ R.A 4J.}nJv/•..~) !J t: / <;" (;. J tJ) -1 b .z: /S (I' ') 4~~'""# Answer: .

b)- The time elapsed since the beginning of the experiment, when we observe 900 bacteria (show

your work)(4 marks) , 1z. ~ ;X::: 0{ (b! GO . \ "- 3}. L9{)o = jt;(l )0) ""-&6 I.' V MotifS60 = (lso)x!L

(p (0-);<'/2-- =- -'1% /.5 ~ Answer: -----'-"-

CST 11 - MATH MCU504: Major Assignment / Math of Finance/ Exponential and Logarithm Functions Page 6

18. The water tower ofBelleville evaporated losing 0.8 % of its volume every halfhour. After howmany hours will the water tower contains 4000 L of water if it initially contained 6250 L? (Show~OU;~(4i~kB~D{!_D.bO$ r >0 ' .~~ ,; £Cues

tr(~ uJre, -? 4000 _ tzso (0. qq'L)--;-j >£ ~--z"rC4000~-f 2fV)7' ~J6 • Y

~? o,cij1L

Answer: c2 7. 7g ~

19. The population of Gatineau recorded in the 2011 census was 314,501. It is expected to increase by2.5% every 6 months. After how many years, rounded to the tenth, will the population of Gatineaube 600,000? (Show you work) (4 marks) 2~'

I1f~dn! .!J == 311{)D/ (!.02~) ~y-;; bOO f)()O c: ZILf 9J / (/.OLJ)

!i'Jtf(bOOO{)O-!- 'S1/.fS7)/) ---?<=7 c2,X.:::- ~

Loo (). D zs:)

20, ()CJ -7 j~

/5~Answer:

20. Talia planned to buy a car for $23 500. She predicts that the value of the car will depreciate by15% per year. After how many years will the car be worth12 500? (Show you work) (4 marks)

3.gg ~t{0;Answer: U---

CST 11 - MATH MCU504: Major Assignment I Math of Financel Exponential and Logarithm Functions Page 7

21. Currently, the population ofthe town ofSwanlake is 7,860. Because of its pristine country-side,flora and fauna, it attracts many new dwellers. The population ofSwanlake is projected toincreases by 3.4% every year. On the other hand, the population of Lone Oak, with currently39,300 inhabitants, decreases by 6% every year. If this trend continues, after how many yearswill the two towns have the same population? (show your work and round you answer to thenearest tenth) (10 marks)

)w~ ~ f ~~rn L,t1~()~ ~~ =- 78£0 (l. 03'1) Y (J ~?p.po (0.94) ~

TJz ~o tN/lF ~J:t1~ [h~if~~

~ (}~(r-7'36o(j.O?'Lf/ ~f$OD [0.94) )<

7~6o )8£0_) (). D?'~] f ~ ~ (0.'1'-1) 'f

(O,q4) )( (O·qLf)>t

(l 0 ~~ Xt&·9'1

~!t ~-X ----+7--9- --

L"(; C /. D S Lt -.!; 0·9 If)

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