# Worksheet: The Net Change Theorem

In this worksheet, we will practice applying the net change theorem.

Q1:

True or False? The Net Change Theorem says that .

• Atrue
• Bfalse

Q2:

True or False: If represents the rate of change of a cat’s weight in kilograms per month when it is months old, then equals the cat’s weight when it is 4 months old.

• Atrue
• Bfalse

Q3:

True or False: The net change theorem states that .

• ATrue
• BFalse

Q4:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A31 m
• B2 m
• C7 m
• D m

Q5:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A m
• B2 m
• C m
• D m
• E m

Q6:

Suppose that . Evaluate using the net change theorem.

Q7:

An oil tanker leaks at the rate liters per minute, where is the number of minutes after the accident. Write an integral that expresses the volume of oil leaked out in the first hour.

• A
• B
• C
• D
• E

Q8:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A60 m
• B m
• C m
• D m
• E6 m

Q9:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A15 m
• B m
• C m
• D m
• E3 m

Q10:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A m
• B14 m
• C m
• D6 m
• E m

Q11:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A m
• B35 m
• C4 m
• D10 m
• E m

Q12:

A particle’s velocity in meters per second as a function of time is . What distance does it travel between and ?

• A m
• B20 m
• C2 m
• D4 m
• E m

Q13:

A piston moves back and forth in one direction. The velocity of the piston (in m/s) can be modeled by the function , where is the time in seconds. What is the change in the position of the piston from to ?

• A5 m
• B m
• C10 m
• D0 m
• E m

Q14:

The rate of growth of a population is represented by the function , where is the number of days after the start of the year. How might the difference in population from to be represented using an integral?

• A
• B
• C
• D
• E

Q15:

If is the acceleration of a car, what does represent?

• AThe total distance the car has traveled from to .
• BThe velocity of the car at .
• CThe position of the car at 3.
• DThe change in the acceleration of the car from to .
• EThe change in the velocity of the car from to .

Q16:

Water is poured in a tank at a rate of liters per hour. The tank contains a hole from which water leaks at a rate of liters per hour. Given that the tank is initially empty, find the total amount of water in the tank after 3 hours. Give your answer to the nearest liter.

Q17:

True or False: The net change theorem states that .

• ATrue
• BFalse

Q18:

The water temperature in a water bath changes at a rate of , where is measured in degrees Celsius per hour and is the time in hours. What is the change in the water temperature from to ?

• A
• B
• C
• D
• E

Q19:

A tank is filled with water at a rate of cubic meters per minute. Find the amount of water that will be filled in the tank from to minutes. Round the answer to one decimal place.

Q20:

The growth rate for the number of bacteria in a sample is given by , where is the time in hours. Assuming no bacteria die, which of the following is an expression for the change in the number of bacteria, , from to ?

• A
• B
• C
• D
• E

Q21:

If is the rate of growth of a child in grams per week, what does represent?

• AIt represents the child’s weight (in grams) at the age of 3 weeks.
• BIt represents the child’s weight (in grams) at the age of 5 weeks.
• CIt represents the child’s weight (in grams) at the age of 1 week.
• DIt represents the increase in the child’s weight (in grams) during the last week.
• EIt represents the net change in the child’s weight (in grams) between the ages of 1 and 5 weeks.

Q22:

If oil leaks from a tank at a rate of gallons per minute at time , which of the following does represent?

• AThe number of gallons of oil left in the tank after 120 minutes
• BThe number of gallons of oil leaked between the and minutes
• CThe number of gallons of oil left in the tank after 20 minutes
• DThe number of gallons of oil left in the tank after 70 minutes
• EThe number of gallons of oil leaked during the last minute

Q23:

A honeybee population starts with 100 bees and increases at a rate of bees per week. What does represent?

• AIt represents the total population in week 16.
• BIt represents the net change in population between week 1 and week 16.
• CIt represents the net change in population between week 1 and week 8.
• DIt represents the total population in week 1.
• EIt represents the total population in week 8.