Question 1

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. ​

Accepted Answer

To calculate the take-home pay after taxes, subtract the taxes from the hourly wage. Taxes are 32% of $28, which is $28 * 0.32 = $8.96. Subtracting this from the hourly wage, $28 - $8.96 = $19.04.

Question 2

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.

Accepted Answer

The answer of A balloon is initially full of air,...

Question 3

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? ​​

Accepted Answer

The answer of You are considering buying three stocks, Stock...

Question 4

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  .
​

Accepted Answer

The answer of A balloon is initially full of air,...

Question 5

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.

Accepted Answer

The answer of The acceleration due to gravity near the...

Question 6

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? ​  ​​

Accepted Answer

The answer of The CEO of a tire company has...

Question 7

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  ?​ ​​

Accepted Answer

The answer of Let B denote the price of a...

Question 8

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? ​  ​

Accepted Answer

The answer of The CEO of a tire company has...

Question 9

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  ? ​​

Accepted Answer

The answer of Let B denote the price of a...

Question 10

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

Accepted Answer

The answer of Let  denote sales when a dollars...

Question 11

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.

Accepted Answer

The answer of You are driving with your cruise control...

Question 12

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

Accepted Answer

The answer of Let  denote sales when a dollars...

Question 13

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.
​

Accepted Answer

The answer of You are driving with your cruise control...

Question 14

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

Accepted Answer

The answer of Let  denote sales when a dollars...

Question 15

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

Accepted Answer

When you press on the accelerator to increase your velocity, your acceleration is positive because acceleration is defined as the rate of change of velocity, and an increase in velocity indicates a positive change.

Question 16

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  ? ​​

Accepted Answer

The answer of Let B denote the price of a...

Question 17

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

Accepted Answer

The answer of Consider a function  .If  is...

Question 18

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

Accepted Answer

The answer of Consider a function  .If  is...

Question 19

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  ? ​

Accepted Answer

The answer of Let B denote the price of a...

Question 20

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

Accepted Answer

Acceleration is negative because it is in the opposite direction of the velocity, indicating a decrease in speed.

Quiz 28: Rates of Change for Other Functions

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. ​

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? ​​

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.

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? ​ ​​

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 ?​ ​​

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? ​ ​

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 ? ​​

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

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.

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

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

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

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 ? ​​

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

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

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 ? ​

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

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.

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?

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?

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 ?

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?

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 ?

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

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

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

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

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 ?

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

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

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 ?

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