The problem set below is meant to be completed as a small group activity (groups of 2 or 3 people). Each group should submit a single set of solutions. Answers should be in sentences, where appropriate. Place the name of each group member on the top of your answer sheet. No work or answers should be submitted on the question papers. Toy stores have discovered that the number of Teenage Mutant Ninja Turtles Deluxe toys 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 at

the same price 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. Verify your answer to question 6 by graphing the function you obtained in

question 5 on the graphing calculator. Call your teacher over to see your group’s calculator screen.

Math 1101 Group Practice – Section 2.3

Solutions to Teenage Mutant Ninja Turtles Deluxe Practice Problems

1. N = 78 – 1.3(40) = 26. K-Mart will sell 2,600 Teenage Mutant

Ninja Turtles Deluxes in a month if they charge $40 per toy.

2. Since N = 37, 37 = 93 – 1.6P –56 = –1.6P 35 = P 3. 78 – 1.3P = 93 – 1.6P .3P = 15 P = 50 78 – 1.3(50) = 13 4. 5. N = 93 – 1.6P N – 93 = – 1.6P

1.6

93N

= P

6. 5625.461.6

935.81

7.

Answer could also be P1.6

N93

Therefore, Toys “R” Us will sell 3700 toys if they charge $35 per toy.

Both stores charged $50 per toy and each sold 1,300 Teenage Mutant Ninja Turtles Deluxes.

Toys “R” Us should charge $46.56 per toy in order to sell 1850 toys.

Using the table

Answers to even-numbered HW problemsSection 2.3

S-4 x = 3.625 or

Ex 18 a) t =

b) She will weigh 68 pounds at age 8.5 years.

c) i. She will be 55.3 inches tall when she weighs 68 pounds.

ii. h = .225w + 40 or h = w + 40

w8

1.88

29 8

Washington State: USDA Climate Zones

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

Make a graph of W versus R. Use a horizontal scale from 3 to 25.

ReRRW 190935. 2 ReRRW 190935. 2

The state of Washington is one of world’s largest producers of grapes. The grapes grown in the state are used to make both wine and grape juice. However, wine is more profitable. One of the reasons the state has been so successful in the production of wine is the relatively dry climate in the central part of the state. If there is too little rain, the grape crop suffers. If there is too much rain, grapes are still produced, but they are unsuitable for making wine and are used in the manufacture of grape juice. Wine industry experts have developed a model for the number of barrels of wine produced per acre as a function of the average number of inches of rainfall per year.

The model is

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

Make a graph of W versus R. Use a horizontal scale from 3 to 25.

ReRRW 190935. 2 ReRRW 190935. 2

The state of Washington is one of world’s largest producers of grapes. The grapes grown in the state are used to make both wine and grape juice. However, wine is more profitable. One of the reasons the state has been so successful in the production of wine is the relatively dry climate in the central part of the state. If there is too little rain, the grape crop suffers. But, if there is too much rain, grapes are still produced, but they are unsuitable for making wine and are used in the manufacture of grape juice. Wine industry experts have developed a model for the number of barrels of wine produced per acre as a function of the average number of inches of rainfall per year.

The model is

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

ReRRW 190935. 2

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

W(14) represents the number of barrels of wine produced per acre if there are 14 inches of rainfall. W(14) = 57.4

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

ReRRW 190935. 2

23 barrels per acre will be produced with 3.63 inches or 22.84 inches of rain.

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

W(14) represents the number of barrels of wine produced per acre if there are 14 inches of rainfall. W(14) = 57.4

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

ReRRW 190935. 2

23 barrels per acre will be produced with 3.63 inches or 22.84 inches of rain.

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

W(14) represents the number of barrels of wine produced per acre if there are 14 inches of rainfall. W(14) = 57.4

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

ReRRW 190935. 2

23 barrels per acre will be produced with 3.63 inches or 22.84 inches of rain.

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

W(14) represents the number of barrels of wine produced per acre if there are 14 inches of rainfall. W(14) = 57.4

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

ReRRW 190935. 2

23 barrels per acre will be produced with 3.63 inches or 22.84 inches of rain.

1. Explain what is meant by W(14) and find its value.

2. If, in a certain year, the wine production was 23 barrels per acre, what does the model indicate the amount of rainfall was that year? Answer to the nearest hundredth of an inch.

3. What amount of rainfall will produce the highest number of barrels of wine per acre? Answer to the nearest hundredth of an inch.

W(14) represents the number of barrels of wine produced per acre if there are 14 inches of rainfall. W(14) = 57.4

12.86 inches of rain will produce the highest number of barrels (57.86).

Where R = number of inches of rainfall per year and W = number of barrels of wine produced per acre.

ReRRW 190935. 2

At birth, the average tyrannosaurus was 3 feet long. A full grown T-Rex could be as much as 50 feet long. Paleontologists have formulated a model that identifies the approximate weight of a tyrannosaurus as a function of its overall length during the T-Rex’s lifetime. That model is given by the function

where W = weight in tons, and L = length in feet.

L02.e371

L10W

1. Make a graph of W versus L.

2. What was the approximate weight of a tyrannosaurus at birth?

3. To the nearest tenth of a foot, how long would an 11 ton tyrannosaurus be?

At birth, the average tyrannosaurus was 3 feet long. A full grown T-Rex could be as much as 50 feet long. Paleontologists have formulated a model that identifies the approximate weight of a tyrannosaurus as a function of its overall length during the T-Rex’s lifetime. That model is given by the function

where W = weight in tons, and L = length in feet.

1. Make a graph of W versus L.

2. What was the approximate weight of a tyrannosaurus at birth?

3. To the nearest tenth of a foot, how long would an 11 ton tyrannosaurus be?

.84 tons

L02.e371

L10W

At birth, the average tyrannosaurus was 3 feet long. A full grown T-Rex could be as much as 50 feet long. Paleontologists have formulated a model that identifies the approximate weight of a tyrannosaurus as a function of its overall length during the T-Rex’s lifetime. That model is given by the function

where W = weight in tons, and L = length in feet.

1. Make a graph of W versus L.

2. What was the approximate weight of a tyrannosaurus at birth?

3. To the nearest tenth of a foot, how long would an 11 ton tyrannosaurus be?

.84 tons

25.5 ft

L02.e371

L10W

32.321.83.18 2 ppG

1. Make a graph of G versus p as the price per gallon rose from $2.60 to 4.20 per gallon. (Suggestion: first adjust the TBLSET menu so that Tbl = .1)

2. How many gallons were consumed daily when the average price of gasoline was $3.50 per gallon?

3. At what price per gallon was gasoline consumption highest (answer to the nearest penny)?

4. At what price(s) per gallon was daily gasoline consumption 3.0 million gallons (answer to the nearest penny)?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

1. Make a graph of G versus p as the price per gallon rose from $2.60 to 4.20 per gallon. (Suggestion: first adjust the TBLSET menu so that Tbl = .1)

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

1. Make a graph of G versus p as the price per gallon rose from $2.60 to 4.20 per gallon. (Suggestion: first adjust the TBLSET menu so that Tbl = .1)

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

2. How many gallons were consumed daily when the average price of gasoline was $3.50 per gallon?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

2. How many gallons were consumed daily when the average price of gasoline was $3.50 per gallon?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

5.045 million gallons

32.321.83.18 2 ppG

3. At what price per gallon was gasoline consumption highest (answer to the nearest penny)?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

3. At what price per gallon was gasoline consumption highest (answer to the nearest penny)?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

$3.43 per gallon

32.321.83.18 2 ppG

4. At what price(s) per gallon was daily gasoline consumption 3.0 million gallons (answer to the nearest penny)?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

32.321.83.18 2 ppG

4. At what price(s) per gallon was daily gasoline consumption 3.0 million gallons (answer to the nearest penny)?

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

$2.62 per gallon

1. Make a graph of G versus p as the price per gallon rose from $2.60 to 4.00 per gallon.

2. How many gallons were consumed daily when the average price of gasoline was $3.50 per gallon?

3. At what price per gallon was gasoline consumption highest (answer to the nearest penny)?

4. At what price(s) per gallon was daily gasoline consumption 3.0 million gallons (answer to the nearest penny)?

$3.43 per gallon

$2.62 per gallon

32.321.83.18 2 ppG

5.045 million gallons

As summer, 2010 approached, demand for gasoline increased, and so did the average price per gallon nationwide. Eventually, when the price of gasoline got high enough, people limited their driving and demand decreased. The function below gives the daily gasoline consumption, G, in millions of gallons as a function of the average price per gallon, p, nationwide in summer 2010.

Homework:

Read section 2.4 (through top of page 175)

Page 180 # S-1, S-5

Page 181 # 5, 6

Read section 2.5 (through top of page 191)

Page 196 # S-1, S-8

Pages 197 – 201 # 2, 18,19

Print and complete PRACTICE TEST 1