Supplemental Instruction (S I ) schedule: Wednesdays from 5:00-6:00 pm

Supplemental Instruction (SI) schedule:

Wednesdays from 5:00-6:00 pm Mondays from 6:30-7:30 pm

in Room 461 in the Burris Library.

The first Supplemental Instruction Session will be tomorrow (August 27)

y = Year K = KSU Enrollment1998 12,8612002 15,6542005 18,5562009 22,389

The table shows the enrollment at Kennesaw State University in various years.

Assuming the enrollment at KSU increased at a constant rate during each time period, answer each of the following questions about the function K = K(y).

Exit Ticket

Source: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books

1. Explain the meaning of K(1998) in this setting and give its value.

2.Estimate the value of K(2000).

3.What is the average rate of change between 2005 and 2009?

4.Use your answer to question 3 to estimate the enrollment at KSU in 2008.


Exit Ticket



2. Estimate the value of K(2000).

3. What is the average rate of change between 2005 and 2009?

4. Use your answer to question 3 to estimate the enrollment at KSU in 2008.

K(1998) means the enrollment at KSU in 1998. It’s value is 12,861


14,258 students

Year KSU Enrollment1970 1,5701971 1,7731972 1,8481973 2,0311974 2,2411975 3,0981976 3,2111977 3,4441978 3,8251979 4,1341980 3,9031981 4,1951982 4,7991983 5,383


Year KSU Enrollment1998 12,8611999 13,1582000 13,373 2001 13,9512002 15,6542003 17,4852004 17,9612005 18,5562006 19,8542007 20,6072008 21,4492009 22,3892010 23,4522011 24,175

Sources: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/

http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf

http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/










Exit Ticket



2. Estimate the value of K(2000).

3. What is the average rate of change between 2005 and 2009?

4. Use your answer to question 3 to estimate the enrollment at KSU in 2008.

K(1998) means the enrollment at KSU in 1998. It’s value is 12,861

Average rate of change from 2005 to 2009 is approximately 958.25 students per year.


KSU enrollment in 2008 was approximately 21,431.

18,556 + 3(958.25)

14,258 students















Practice

Answer each of the following questions about the function M = M(y). Show work.

1. Explain the meaning of M(1975) and give its value.

2. Estimate the value of M(1968).

3. What was the average rate of change in the number of murders from 1970 and 1975?

4. Use your answer to question 3 to estimate the number of murders in the U.S. in 1973.

The table at the right shows the number of murders reported in the United States in the years listed. Assume that the number of murders in the United States rose uniformly from 1962 through 1980.

y =Year M = Number of Murders in the U.S.

1962 8,530

1966 11,040

1970 17,780

1975 20,510

1980 23,040

1985 18,980 Source: http://www.disastercenter.com/crime/uscrime.htm

http://images.google.com/imgres?imgurl=http://forgotston.com/wp-content/uploads/2007/12/murders1.gif&imgrefurl=http://forgotston.com/2007/12/&usg=__Rot4Dkrq8vEwPMPyP0SH0_7Ui30=&h=265&w=390&sz=9&hl=en&start=8&tbnid=66ruV2c4f3IctM:&tbnh=84&tbnw=123&prev=/images%3Fq%3Dmurder%26gbv%3D2%26hl%3Den

http://www.google.com/imgres?imgurl=http://www.nass.usda.gov/Statistics_by_State/images/us_map_pr.gif&imgrefurl=http://www.nass.usda.gov/Statistics_by_State/&usg=__9pbfdSP3T_-5RWxDj28TvxKIKHw=&h=361&w=571&sz=23&hl=en&start=2&zoom=1&itbs=1&tbnid=nY9bvNRncIhj3M:&tbnh=85&tbnw=134&prev=/images%3Fq%3DU.S.%26hl%3Den%26gbv%3D2%26tbs%3Disch:1

Practice







M(1975) represents the number of murders in the U.S. in 1975. M(1975) = 20,510

M(1968) 14,410

The average rate of change from 1970 and 1975 was 546 murders per year.

The number of murders in the U.S. in 1973 was approximately 19,418.


1962 8,530

1966 11,040

1970 17,780

1975 20,510

1980 23,040

1985 18,980 Source: http://www.disastercenter.com/crime/uscrime.htm

http://images.google.com/imgres?imgurl=http://forgotston.com/wp-content/uploads/2007/12/murders1.gif&imgrefurl=http://forgotston.com/2007/12/&usg=__Rot4Dkrq8vEwPMPyP0SH0_7Ui30=&h=265&w=390&sz=9&hl=en&start=8&tbnid=66ruV2c4f3IctM:&tbnh=84&tbnw=123&prev=/images%3Fq%3Dmurder%26gbv%3D2%26hl%3Den

Practice






5. What was the average rate of change in the number of murders from 1980 and 1985.


M(1975) represents the number of murders in the U.S. in 1975. M(1975) = 20,510

M(1968) 14,410

The average rate of change from 1970 and 1975 was 546 murders per year.

The number of murders in the U.S. in 1973 was approximately 19,418.


1962 8,530

1966 11,040

1970 17,780

1975 20,510

1980 23,040

1985 18,980

The average rate of change from 1980 and 1985 was -812.The average rate of decrease is 812 murders per year.

Answers to even-numbered HW problems S-8 20.7

Ex 8 a) A(75) means the temperature of a piece of aluminum 75 minutes after it has been removed from the oven. A(75) = 90.5

b) The average decrease per minute is 5

c) The average decrease per minute is .63

d) The rate of cooling is slowing down as the aluminum cools and its temperature approaches room temperature.

e) A(73) = 91.8

f) The temperature of the oven is A(0) = 302.

Ex 10 a)

Section 1.2

t = year B = Vaue

1996 615.9

1999 769.5

2002 876.8

2005 1143.7

51.2

35.8

89.0

b) B(2004) means the number of billions of dollars in new construction in the U.S. in the year 2004. B(2004) = 1,054.8 billion.

c) 2002 – 2005 d) 2005

S = Standing Time

(in minutes)

T = Temperature

(in degrees Fahrenheit)

0 32

3 45

6 56

9 65

12 73

15 78

18 82

21 83.5

24 84

27 84

Trends and Limiting Values

Here, the limiting value appears to be approximately 84.

The limiting value of a function (if there is one) is a number that the function (output) values appear to get closer to as the input values get larger and larger.

• As a graph

Last class we said:

A function can be represented in several ways, including: As a formula

As a set of number pairs

As a table

As an arrow diagram

Year Number of Deaths


1981 128 1988 21,040

1982 460 1989 27,691

1983 1,501 1990 31,402

1984 3,497 1991 36,307

1985 6,961 1992 40,516

1986 12,056 1993 42,992

1987 16,336 1994 46,050

Source: United States Centers for Disease Control and Prevention, HIV/AIDS Surveillance Report, Year-End Edition 1995


1995 47,414

1996 38,074

1997 21,846

1998 19,005

1999 18,491

2000 17,139

Number of Deaths from AIDS in the United States by Year

Represent the relationship between the year and the number of AIDS deaths by D = D(y), where y = the year, and D = the number of deaths.



1981 128 1988 21,040

1982 460 1989 27,691

1983 1,501 1990 31,402

1984 3,497 1991 36,307

1985 6,961 1992 40,516

1986 12,056 1993 42,992

1987 16,336 1994 46,050


1995 47,414

1996 38,074

1997 21,846

1998 19,005

1999 18,491

2000 17,139

Number of Deaths from AIDS in

the United States by Year

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000

y = year

D(y

) =

num

ber

of d

eath

s

12,056



1981 128 1988 21,040

1982 460 1989 27,691

1983 1,501 1990 31,402

1984 3,497 1991 36,307

1985 6,961 1992 40,516

1986 12,056 1993 42,992

1987 16,336 1994 46,050


1995 47,414

1996 38,074

1997 21,846

1998 19,005

1999 18,491

2000 17,139



D(1986) = 12,056

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000

y = year

D(y

) =

num

ber

of d

eath

s



1981 128 1988 21,040

1982 460 1989 27,691

1983 1,501 1990 31,402

1984 3,497 1991 36,307

1985 6,961 1992 40,516

1986 12,056 1993 42,992

1987 16,336 1994 46,050


1995 47,414

1996 38,074

1997 21,846

1998 19,005

1999 18,491

2000 17,139



50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000


y = year

D(y

) =

num

ber

of d

eath

s

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000


y = year

D(y

) =

num

ber

of d

eath

s

Questions:

1. Use the graph to estimate the value of D(1991) and explain its meaning.

D(1991) means the number of deaths due to AIDS in the U.S. in 1991. From the graph, D(1991) is approximately 36,000.



1981 128 1988 21,040

1982 460 1989 27,691

1983 1,501 1990 31,402

1984 3,497 1991 36,307

1985 6,961 1992 40,516

1986 12,056 1993 42,992

1987 16,336 1994 46,050

●

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000


y = year

D(y

) =

num

ber

of d

eath

s

The maximum number of AIDS deaths occurred in 1995 and was approximately 47,500.

●

Questions:

2. In what year did the maximum number of AIDS deaths occur and what was that number?


1995 47,414

1996 38,074

1997 21,846

1998 19,005

1999 18,491

2000 17,139

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000


y = year

D(y

) =

num

ber

of d

eath

s

The number of AIDS deaths decreased from 1995 to 2000.

Questions:

3. During which years were the number of AIDS deaths decreasing? Between what 2 years was the decrease most rapid?

The most rapid decrease was between 1995 and 1997.

Stock Market Performance The Dow Jones Industrial

Average

Properties of graphs:

• Increasing or decreasing

• Concavity

• Points of Inflection

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

Dow

Jon

es A

vera

ge

(in t

hous

ands

of

dol

lars

)

10

11

12

13

9

It is an index that shows how 30 large, publicly owned companies based in the United States have traded during a standard trading session in the stock market.

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

Dow

Jon

es A

vera

ge

(in t

hous

ands

of

dol

lars

)

10

11

12

13

9


Average


• Increasing or decreasing

The function increases from 2000 to 2001, and from 2004 to 2008,

The function decreases from 2001 to 2004 and after 2008.


Average

9,200

12,000

To determine when increase (or decrease) is more rapid over equal time periods, compare the change in value.

Change in value:

2000-01 12,000 – 9,000 = $3,000

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

Dow

Jon

es A

vera

ge

(in t

hous

ands

of

dol

lars

)

10

11

12

13

11,000

9

During which years was the Dow Jones increasing more rapidly – from 2000 to 2001 or from 2005 to 2006?

2005-06 11,000 – 9,200 = $1,800


Average

9,200

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

Dow

Jon

es A

vera

ge

(in t

hous

ands

of

dol

lars

)

10

11

12

13

11,000

9


13,300

Change in value:

2005-06 800,1200,9000,11

2006-08 300,2000,11300,13


Average

9,200

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

10

11

12

13

11,000

9


To determine when increase (or decrease) is more rapid regardless of the time interval, compute the average rate of change for each interval. The interval with the larger average rate of change is increasing (or decreasing) more rapidly.

13,300

Average rate of change:

2005-06 800,11

200,9000,11

2006-08 150,12

000,11300,13

Average weekly gas prices in the Metro Atlanta area from May 1, 2008 – Nov 1, 2008

Week

Price per

Gallon in

Dollars

2.60

2.80

3.00

3.20

3.40

3.60

3.80

4.00

4.10

4.20

2 4 6 8 10 12 14 16 18 20 22 24


Concavity

or

This section is Concave up

or

This section is Concave down

Point of Inflection


Average

2000 2001 2002 2003 2004 2005 2006 2007 2008

y = year

Dow

Jon

es A

vera

ge

(in t

hous

ands

of

dol

lars

)

10

11

12

13

9

Does this graph have a point of inflection?

Homework:

Read Section 1.3 (omit pages 69-74)

Page 75 # S-1 through S-10

Pages 76–79 # 2, 5, 11

Documents

Supplemental Instruction (S I ) schedule: Wednesdays from 5:00-6:00 pm