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.}\\).

Explanation:

Identify the variables

Using the Independent and Dependent Variables knowledge point

$$
LATEXBLOCK0
$$

Determine the rate of change

Using the Rate of Change Interpretation knowledge point

$$
LATEXBLOCK1
$$

Match with the correct statement

The dependent variable (water depth) varies with respect to the independent variable (time) at a rate of \(-9\text{ in./week}\). This corresponds to option A.

Answer:

• (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 \(-9\text{ week/in.}\)