Deck 28: Rates of Change for Other Functions

Question 1

Consider a function .Suppose .What can be said about the function f? ​

A) f is a linear function with slope -7.
B) f is an exponential function with growth factor 7.
C) f is a linear function with slope 7.
D) None of the above.

Answer 1

f is a linear function with slope 7.

Question 2

If is positive then the function is certain to be positive.

Answer 2

False

Question 3

Consider a function .When is increasing, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) is increasing.

Answer 3

is positive.

Question 4

If denotes the profit earned from an investment of I dollars, then represents the marginal profit.

Question 5

The marginal profit is the additional profit earned on each additional dollar of investment.

Question 6

Consider a function .When f is not changing, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) is increasing.

Question 7

Consider a function .If the graph of f is constant, neither increasing nor decreasing, what can be said about the graph of ? ​

A) The graph of is above the horizontal axis.
B) The graph of is below the horizontal axis.
C) The graph of lies on the horizontal axis.
D) The graph of is increasing.

Question 8

Consider a function .If the graph of f is increasing, what can be said about the graph of ? ​

A) The graph of is above the horizontal axis.
B) The graph of is below the horizontal axis.
C) The graph of lies on the horizontal axis.
D) The graph of is increasing.

Question 9

Consider a function .If the graph of f is decreasing, what can be said about the graph of ? ​

A) The graph of is above the horizontal axis.
B) The graph of is below the horizontal axis.
C) The graph of lies on the horizontal axis.
D) The graph of is decreasing.

Question 10

At a minimum value of , is 0.

Question 11

If denotes the tax owed on an income of I dollars, then represents the marginal tax rate.

Question 12

The marginal tax rate is the additional tax owed on each additional dollar of income.

Question 13

At a maximum value of , is negative.

Question 14

Consider a function .When f is decreasing, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) is increasing.

Question 15

The rate of change in velocity is acceleration.

Question 16

If is negative then the function is decreasing.

Question 17

You are driving with your cruise control set.What can be said regarding your acceleration? ​

A) Acceleration is 0.
B) Acceleration is positive.
C) Acceleration is negative.
D) Acceleration is increasing.

Question 18

Consider a function .If the graph of is above the horizontal axis, what can be said about the graph of f? ​

A) The graph of f is above the horizontal axis.
B) The graph of f is below the horizontal axis.
C) The graph of f is increasing.
D) The graph of f is a straight line.

Question 19

Consider a function .If the graph of is constant, neither increasing nor decreasing, what can be said about the graph of f? ​

A) The graph of f is above the horizontal axis.
B) The graph of f is below the horizontal axis.
C) The graph of f lies on the horizontal axis.
D) The graph of f is a straight line.

Question 20

Consider a function .If the graph of is below the horizontal axis, what can be said about the graph of f? ​

A) The graph of f is above the horizontal axis.
B) The graph of f is below the horizontal axis.
C) The graph of f is decreasing.
D) The graph of f is a straight line.

Question 21

You have the opportunity to earn some extra income by working at $28 per hour.If your marginal tax rate is 32%, how much of the hourly income will you take home after taxes? Round your answer to two decimal places, if necessary. ​

A) $28
B) $32
C) $19.04
D) $8.96

Question 22

A balloon is initially full of air, but then it springs a leak.Air leaks at a constant rate from the balloon.After a while the leak is patched and a pump is attached to the balloon.It is re-inflated to its original volume: Air is pumped at a constant rate that is larger than the rate of the leak.Let B denote the volume, in cubic inches, of air in the balloon after t minutes.Make a graph of B versus t from the time the balloon springs a leak until it is fully re-inflated.

Question 23

You are considering buying three stocks, Stock 1, Stock 2, and Stock 3, and their prices at time t are given by , , and , respectively.You observe that is positive, is near 0, and is negative.Which stock is likely to provide the best growth in the short term? ​​

A) Stock 1
B) Stock 2
C) Stock 3
D) None of the above.

Question 24

A balloon is initially full of air, but then it springs a leak.Air leaks at a constant rate from the balloon.After a while the leak is patched and a pump is attached to the balloon.It is re-inflated to its original volume: Air is pumped at a constant rate that is larger than the rate of the leak.Let B denote the volume, in cubic inches, of air in the balloon after t minutes.The graph of B versus t from the time the balloon springs a leak until it is fully re-inflated is shown.Make the graph of .
​

Question 25

The acceleration due to gravity near the surface of Earth has a constant value of 32 feet per second per second.Explain what this fact tells us about the downward velocity of a falling object near the surface of Earth.

Question 26

The CEO of a tire company has kept records for the profit P when n tires are produced.The rate of change is the marginal profit.The graph of marginal profit is shown.If the current rate of production is 180 tires, what effect on profit will an increase in production have? ​ ​​

A) Profits will be increased.
B) Profits will remain the same.
C) Profits will be reduced.
D) None of the above

Question 27

Let B denote the price of a bag of groceries at time t.It is found that is negative at .What can be concluded about the graph of B at the point ?​ ​​

A) The price of groceries reaches a maximum at .
B) The price of groceries reaches a minimum at .
C) The price of groceries is increasing at .
D) The price of groceries is decreasing at .

Question 28

The CEO of a tire company has kept records for the profit P when n tires are produced.The rate of change is the marginal profit.The graph of marginal profit is shown.According to the graph, how many tires per day should the company be producing in order to maximize profit? ​ ​

A) 150
B) 270
C) 30
D) None of the above

Question 29

Let B denote the price of a bag of groceries at time t.It is found that is positive at .What can be concluded about the graph of B at the point ? ​​

A) The price of groceries reaches a maximum at .
B) The price of groceries reaches a minimum at .
C) The price of groceries is increasing at .
D) The price of groceries is decreasing at .

Question 30

Let denote sales when a dollars are spent on advertising.We find that s has reached its maximum value.What is the value of ? ​​​

A) is positive.
B) is negative.
C) is 0.
D) The value of cannot be determined.

Question 31

You are driving with your cruise control set when you encounter a slowly moving truck.You speed up to pass the truck.When you have overtaken the truck, you slow down and resume your previous speed.If represents your velocity at time t, make a graph of .Be sure to label your graph appropriately.

Question 32

Let denote sales when a dollars are spent on advertising.If is positive, what will be the effect on sales if advertising is increased? ​​

A) Sales will increase.
B) Sales will decrease.
C) Sales will remain the same.
D) None of the above

Question 33

You are driving with your cruise control set when you encounter a slowly moving truck.You speed up to pass the truck.When you have overtaken the truck, you slow down and resume your previous speed.The graph of velocity, , is shown.Make a graph of , the acceleration.Be sure to label your graph appropriately.
​

Question 34

Let denote sales when a dollars are spent on advertising.If is negative, what will be the effect on sales if advertising is increased? ​

A) Sales will increase.
B) Sales will decrease.
C) Sales will remain the same.
D) None of the above

Question 35

You are driving and press on the accelerator to increase your velocity.What can be said regarding your acceleration? ​

A) Acceleration is 0.
B) Acceleration is positive.
C) Acceleration is negative.
D) Acceleration is increasing.

Question 36

Let B denote the price of a bag of groceries at time t.It is found that changes sign from negative to positive at .What can be concluded about the graph of B at the point ? ​​

A) The graph of B reaches a maximum at .
B) The graph of B reaches a minimum at .
C) The graph of B is increasing at .
D) The graph of B is decreasing at .

Question 37

Consider a function .If is constant and negative, what can be said about the function f? ​

A) f is linear with positive slope.
B) f is linear with negative slope.
C) f is constant and positive.
D) f is constant and negative.

Question 38

Consider a function .If is constant and positive, what can be said about the function f? ​

A) f is linear with positive slope.
B) f is linear with negative slope.
C) f is constant and positive.
D) f is constant and negative.

Question 39

Let B denote the price of a bag of groceries at time t.It is found that changes sign from positive to negative at .What can be concluded about the graph of B at the point ? ​

A) The graph of B reaches a maximum at .
B) The graph of B reaches a minimum at .
C) The graph of B is increasing at .
D) The graph of B is decreasing at .

Question 40

You are driving and press on the brake to decrease your velocity.What can be said regarding your acceleration? ​

A) Acceleration is 0.
B) Acceleration is positive.
C) Acceleration is negative.
D) Acceleration is increasing.