# Worksheet: The Net Change Theorem

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

**Q2: **

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

- Atrue
- Bfalse

**Q3: **

True or False: The net change theorem states that .

- ATrue
- BFalse

**Q4: **

A particleβs 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

**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 particleβs 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 particleβs 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

**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 .

**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

**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 childβs weight (in grams) at the age of 3 weeks.
- BIt represents the childβs weight (in grams) at the age of 5 weeks.
- CIt represents the childβs weight (in grams) at the age of 1 week.
- DIt represents the increase in the childβs weight (in grams) during the last week.
- EIt represents the net change in the childβs 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.