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 6 inches per week because of evaporation. how much does the water depth change in 5 weeks? in 15 weeks?

which statement describes this situation?

a. time varies with respect to the water depth with a rate of change of \\(-6\text{ in./week}\\).
b. the water depth varies with respect to time with a rate of change of \\(-6\text{ in./week}\\).
c. time varies with respect to the water depth with a rate of change of \\(-6\text{ week/in.}\\).
d. the water depth varies with respect to time with a rate of change of \\(-6\text{ week/in.}\\).

how much has the water depth changed after 5 weeks?

the water depth has dropdown by box inch(es).
(type an integer or a decimal.)

Explanation:

Identify variables and rate of change

Using the Independent and Dependent Variables and Rate of Change Analysis knowledge points

• Independent variable: Time \(t\) (in weeks)
• Dependent variable: Water depth \(d\) (in inches)
• Rate of change: \(-6\text{ in./week}\) (since depth decreases)
• Statement: The water depth varies with respect to time with a rate of change of \(-6\text{ in./week}\).

Calculate change after 5 weeks

Using the Rate of Change Analysis knowledge point

$$ \Delta d = \text{rate} \times \Delta t = -6\text{ in./week} \times 5\text{ weeks} = -30\text{ inches} $$

This represents a decrease of \(30\text{ inches}\).

Answer:

Question 1

• (A) Time varies with respect to the water depth with a rate of change of \(-6\text{ in./week}\)
• (B) The water depth varies with respect to time with a rate of change of \(-6\text{ in./week}\) (Correct answer)
• (C) Time varies with respect to the water depth with a rate of change of \(-6\text{ week/in.}\)
• (D) The water depth varies with respect to time with a rate of change of \(-6\text{ week/in.}\)

Question 2

The water depth has <blank>decreased</blank> by <blank>30</blank> inch(es).