AnswersFL-1200330-Algebra 2 CRModeling with Rational Functions

Modeling with Rational Functions Answers

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Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club?

Question illustration
A
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Option A
B
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Option B
C
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Option C
D
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Option D
2
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The game commission introduces 200 white-tailed deer into a newly acquired national game and wildlife park. The population of the herd is modeled by the graph of the rational function below, where time is measured in years. Which statement about the population is true?

Question illustration
A
The graph shows that the population of deer will eventually be 0.
B
The rate at which the population of deer grows decreases as it approaches 1,500.
C
The graph shows that the population of deer decreases over time.
D
The rate at which the population of deer grows increases as it approaches 1,500.
3

A 22,800-gallon swimming pool is being filled by four hoses. Water flows through each hose at a rate of 300 gallons per hour. How many hours will it take to fill the pool?

A
19 hours
B
76 hours
C
152 hours
D
304 hours
4

A pharmacist has 80 milliliters of a 30% saline solution. The graph shows the percentage concentration after adding x milliliters of a 10% saline solution. Which statement is true about the graph of the function?

Question illustration
A
The vertical asymptote x = 30 means the concentration will always be less than 30%.
B
The vertical asymptote x = 10 means the volume will always be greater than 10 milliliters.
C
The y-intercept means the concentration will remain 30% if no solution is added.
D
The y-intercept means the concentration will always be less than 30%.
5

A scientist has 40 liters of a 50% acidic solution. She adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. The graph models the percent of acidity in the final mixture. How many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

Question illustration
A
0.5 liters
B
30 liters
C
80 liters
D
37 liters
6

The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years. If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?

Question illustration
A
The chlorine pool is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
B
The saltwater pool is more cost effective because the y-value at 10 years is less on graph A than it is on graph B.
C
They would be equally cost effective because the vertical asymptotes for each graph are the same.
D
They would be equally cost effective because the horizontal asymptotes for each graph are the same.
7

Craig bought a treadmill for $400. He estimates that the annual costs to maintain the machine will be $36. Which rational function yields the average annual cost in dollars of owning the treadmill for x years?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?

Question illustration
A
0.05 in.3
B
0.5 in.3
C
20 in.3
D
200 in.3
9

The function models y, the average annual cost in dollars of owning a car for x years. Which statement best explains why the graph of should have a vertical asymptote at x = 0?

Question illustration
A
The value of the car decreases over time.
B
The value of the car will never dip below $0.
C
The time the car is owned is greater than 0.
D
The initial cost of the car is greater than $0.
10

Greg plans to purchase a bicycle. Bike A costs $270 and has an expected maintenance cost of $36 per year. Bike B costs $360 and has an expected maintenance cost of $20 per year. Which statement is true based on the average annual cost of each bike?

A
Bike A is the better choice if Greg plans on owning the bike for 5 years or 6 years.
B
Bike B is the better choice if Greg plans on owning the bike for 5 years or 6 years.
C
Bike A is the better choice if Greg plans on owning the bike for 5 years. Bike B is the better choice if Greg plans on owning the bike for 6 years.
D
Bike B is the better choice if Greg plans on owning the bike for 5 years. Bike A is the better choice if Greg plans on owning the bike for 6 years.
11

A scientist has 40 liters of a 50% acidic solution. She adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. The graph models the percent of acidity in the final mixture. How many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

Question illustration
A
0.5 liters
B
30 liters
C
80 liters
D
37 liters
12

Sarah plans to sell homemade birdhouses at the local craft fair. She spent $90 on new tools and estimates that she spends $6 in materials for each birdhouse. Which rational function models the average cost per birdhouse, y, in dollars of building x birdhouses?

A
mc007-1.jpg
Option A
B
mc007-2.jpg
Option B
C
mc007-3.jpg
Option C
D
mc007-4.jpg
Option D
13

The function yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function?

Question illustration
A
The company spends $600 on a new computer and printer before beginning the project.
B
The company takes 600 photos before selecting which ones to use for its calendars.
C
The company expects to sell 600 calendars each month.
D
The company will sell the calendars for $2.00 each.
14

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A charges 4% interest over 6 years. Plan B charges 5% interest over 4 years. The formula can be used to calculate the monthly payment, m, where P is the principle amount borrowed, r is the interest rate expressed as a decimal, and t is the time of the loan, in years. Which statement best compares the plans?

Question illustration
A
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
B
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
C
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
D
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B.
15

The function models y, the average annual cost in dollars of owning a car for x years. Which statement best explains why the graph of should have a vertical asymptote at x = 0?

Question illustration
A
The value of the car decreases over time.
B
The value of the car will never dip below $0.
C
The time the car is owned is greater than 0.
D
The initial cost of the car is greater than $0.
16

Greg plans to purchase a bicycle. Bike A costs $270 and has an expected maintenance cost of $36 per year. Bike B costs $360 and has an expected maintenance cost of $20 per year. Which statement is true based on the average annual cost of each bike?

A
Bike A is the better choice if Greg plans on owning the bike for 5 years or 6 years.
B
Bike B is the better choice if Greg plans on owning the bike for 5 years or 6 years.
C
Bike A is the better choice if Greg plans on owning the bike for 5 years. Bike B is the better choice if Greg plans on owning the bike for 6 years.
D
Bike B is the better choice if Greg plans on owning the bike for 5 years. Bike A is the better choice if Greg plans on owning the bike for 6 years.
17

Louis plans to buy a new washing machine. The washing machine costs $560 and has an estimated annual operating cost of $48. Which rational function models the average annual cost in dollars of owning the washing machine for x years?

A
mc016-1.jpg
Option A
B
mc016-2.jpg
Option B
C
mc016-3.jpg
Option C
D
mc016-4.jpg
Option D
18

Craig bought a treadmill for $400. He estimates that the annual costs to maintain the machine will be $36. Which rational function yields the average annual cost in dollars of owning the treadmill for x years?

A
mc010-1.jpg
Option A
B
mc010-2.jpg
Option B
C
mc010-3.jpg
Option C
D
mc010-4.jpg
Option D
19

The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years. If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?

Question illustration
A
The chlorine pool is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
B
The saltwater pool is more cost effective because the y-value at 10 years is less on graph A than it is on graph B.
C
They would be equally cost effective because the vertical asymptotes for each graph are the same.
D
They would be equally cost effective because the horizontal asymptotes for each graph are the same.
20

A pharmacist has 80 milliliters of a 30% saline solution. The graph shows the percentage concentration after adding x milliliters of a 10% saline solution. Which statement is true about the graph of the function?

Question illustration
A
The vertical asymptote x = 30 means the concentration will always be less than 30%.
B
The vertical asymptote x = 10 means the volume will always be greater than 10 milliliters.
C
The y-intercept means the concentration will remain 30% if no solution is added.
D
The y-intercept means the concentration will always be less than 30%.

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