where n = number reported car thefts in charleston. and t = number of years since 1970

The function below gives an estimate of the number of reported car thefts annually in Charleston, S.C. from 1970 through 2010.

t

2ttN

1.002

17453.5.12 3 where N = number reported car thefts in Charleston.

and t = number of years since 1970

1. Copy and fill in the window at the right for graphing the function N = N(t) from 1970 to 2010.

2.Graph the function on your calculator and use the graph to approximate the number of reported car thefts in Charleston in 1997. CALL YOUR TEACHER OVER TO SEE THE ANSWER ON YOUR CALCULATOR SCREEN. Don’t forget to record your answer.

3.Based on the function, in what year did the number of car thefts in Charleston go above 2,500?

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t

2ttN

1.002




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0405

10004000500

1


t

2ttN

1.002





_________________________________________________

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0405

10004000500

1


t

2ttN

1.002





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0405

10004000500

1

Based on the function, there were about 1474 car thefts reported in Charleston in 1997.


t

2ttN

1.002



3.Based on the function, in what year did the number of car thefts in Charleston go above 2,500?

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0405

10004000500

1

Based on the function, the number of car thefts in Charleston first went above 2,500 in 2006.

Answers to even-numbered HW problems Section 2.2

S-12

Ex 4 a)

b) P(0) = –180. It represents a loss of $180,000.

c) The profit for 15,000 widgets will be $420,000.

d) The break even point is approximately 2,000 widgets.

e) The largest possible profit is approximately $444,000.

Verizon Wireless offers its cell phone customers a variety of plans. Two of them are described below.

Plan 1. $15.00 per month plus 10 cents a minute.

Plan 2. $30.00 per month plus 6 cents per minute.

http://www.verizonwireless.com/b2c/index.html

Using C for cost and N for number of minutes, use a formula to express the cost of plan 1 as a function of the number of minutes used per month.




C = .10N + 15

C = .06N + 30

1. What would be your monthly bill under plan 1 if you spoke for a total of 600 minutes during the month?

Questions: Assuming there are no other costs –






C = .10N + 15

C = .06N + 30


$75







C = .10N + 15

C = .06N + 30








C = .10N + 15

C = .06N + 30

2. If your monthly bill under plan 2 was $42.40, for how many minutes did you speak? Give an algebraic solution.


207 minutes






C = .10N + 15

C = .06N + 30

2. If your monthly bill under plan 2 was $42.40, for how many minutes did you speak? Give an algebraic solution.







C = .10N + 15

C = .06N + 30

3. For how many minutes would you have to speak in a month for the cost of both plans to be the same? Give an algebraic solution and verify using the graphing calculator.


375 minutes





C = .10N + 15

C = .06N + 30

3. For how many minutes would you have to speak in a month for the cost of both plans to be the same? Give an algebraic solution and verify using the graphing calculator.






C = .10N + 15

C = .06N + 30

4. In Plan 2, C is expressed as a function of N. Write a formula for Plan 2 expressing N as a function of C.


.06

30CN

5. How many minutes would you have to speak in a month for the cost with Plan 2 to be $90? How many minutes for $125? How many minutes for $78.20?





C = .10N + 15

C = .06N + 30

4. In Plan 2, C is expressed as a function of N. Write a formula for Plan 2 expressing N as a function of C.


.06

30CN

5. How many minutes would you have to speak in a month for the cost with Plan 2 to be $90? 1,000 minutes

6. Use a graph to verify your answer to # 5

Group Problem Set

The problems on the following slide were completed in class as a graded group assignment. If you were not in class, please complete the problems on your own and turn in your solutions at the beginning of our next class meeting to receive full credit.

Teenage Mutant Ninja Turtles

http://tickleme.tripod.com/sounds.html

Toy stores have discovered that the number of Teenage Mutant Ninja Turtles Deluxetoys sold in a month decreases as the price increases. This means that the number N, in hundreds of Teenage Mutant Ninja Turtles Deluxes sold is a function of the price, P in dollars of each toy. Specifically, at K-Mart, this function is N = 78 – 1.3P. At Toys “R” Us, this function is N = 93 – 1.6P. Neither store will sell Teenage Mutant Ninja Turtles Deluxe for less than $25.

1. How many Teenage Mutant Ninja Turtles Deluxes will K-Mart sell in a month if they charge $40 per toy?

2. What price should Toys “R” Us charge for Teenage Mutant Ninja Turtles Deluxe in order to sell 3,700 of them? Show an algebraic solution.

3. If both stores sold the same number of Teenage Mutant Ninja Turtles Deluxes in March, how many Teenage Mutant Ninja Turtles Deluxes did each store sell and what price did they charge? Show an algebraic solution.

4. Verify your answer to question 3 using the table option on the graphing calculator. Call your teacher over to see your group’s calculator screen.

5. Use the Toys “R” Us formula to obtain a formula expressing P as a function of N.

6. Use your answer to number 5 to determine the price Toys “R” Us should charge in order to sell 1,850 Teenage Mutant Ninja Turtles Deluxes. Show an algebraic solution.

7. Use a graph of the function you obtained in question 5 to verify your answer to question 6. Call your teacher over to see your group’s calculator screen.

Homework:

Read Section 2.3 (through top of page 157)

Page 163 # S-4, S-7, S-9, S-11

Pages 164–168 # 3, 7, 13, 18

where n = number reported car thefts in charleston. and t = number of years since 1970

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