Question

the following situation involves a rate of change that is constant. write a statement that describes how one variable changes with respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer any questions.

the water depth in a lake decreases at a rate of 9 inches per week because of evaporation. how much does the water depth change in 3 weeks? in 14 weeks?

which statement describes this situation?

a. the water depth varies with respect to time with a rate of change of \\(-9\text{ in./week}\\).
b. the water depth varies with respect to time with a rate of change of \\(-9\text{ week/in.}\\).
c. time varies with respect to the water depth with a rate of change of \\(-9\text{ in./week}\\).
d. time varies with respect to the water depth with a rate of change of \\(-9\text{ week/in.}\\).

how much has the water depth changed after 3 weeks?

the water depth has decreased/increased by inch(es).

Explanation:

Identify variables and rate of change

Using the Rate of Change Interpretation knowledge point

• Independent variable: Time \(t\) (measured in weeks)
• Dependent variable: Water depth \(W\) (measured in inches)
• Rate of change: Since the depth decreases by \(9\text{ inches}\) each week, the rate of change is \(-9\text{ in./week}\).
• Statement: The water depth varies with respect to time with a rate of change of \(-9\text{ in./week}\).

Calculate change after 3 weeks

Using the Rate of Change Rule knowledge point

$$ \text{Change} = \text{Rate of change} \times \text{Time} = -9\text{ in./week} \times 3\text{ weeks} = -27\text{ inches} $$

This represents a decrease of \(27\text{ inches}\).

Calculate change after 14 weeks

Using the Rate of Change Rule knowledge point

$$ \text{Change} = \text{Rate of change} \times \text{Time} = -9\text{ in./week} \times 14\text{ weeks} = -126\text{ inches} $$

This represents a decrease of \(126\text{ inches}\).

Answer:

Question 1

• A. The water depth varies with respect to time with a rate of change of \(-9\text{ in./week}\). (Correct answer)
• B. The water depth varies with respect to time with a rate of change of \(-9\text{ week/in.}\)
• C. Time varies with respect to the water depth with a rate of change of \(-9\text{ in./week}\)
• D. Time varies with respect to the water depth with a rate of change of \(-9\text{ week/in.}\)

Question 2

The water depth has decreased by 27 inch(es).

Question 3

The water depth has decreased by 126 inch(es).