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 2 inches per day because of evaporation. how much does the water depth change in 4 days? in 16 days?

which statement describes this situation?
a. time varies with respect to the water depth with a rate of change of -2 day/in.
b. the water depth varies with respect to time with a rate of change of -2 day/in.
c. the water depth varies with respect to time with a rate of change of -2 in./day.
d. time varies with respect to the water depth with a rate of change of -2 in./day.

how much has the water depth changed after 4 days?
the water depth has increased/decreased by inch(es).
(type an integer or a decimal.)

how much has the water depth changed after 16 days?
the water depth has increased/decreased by inch(es).
(type an integer or a decimal.)

Explanation:

Identify variables and rate

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

• Independent variable: Time \(t\) (in days)
• Dependent variable: Water depth \(d\) (in inches)
• Rate of change: \(-2\text{ in/day}\) (since depth decreases by \(2\text{ inches per day}\))

Select the describing statement

Using the Rate of Change Interpretation knowledge point

• The dependent variable (water depth) varies with respect to the independent variable (time).
• The rate of change is \(-2\text{ in/day}\).
• This matches option C: "The water depth varies with respect to time with a rate of change of \(-2\text{ in/day}\)."

Calculate change after 4 days

Using the Rate of Change Rule knowledge point

$$ \Delta d = \text{rate} \times \Delta t = -2\text{ in/day} \times 4\text{ days} = -8\text{ inches} $$

• A change of \(-8\text{ inches}\) means the water depth has decreased by \(8\text{ inches}\).

Calculate change after 16 days

Using the Rate of Change Rule knowledge point

$$ \Delta d = \text{rate} \times \Delta t = -2\text{ in/day} \times 16\text{ days} = -32\text{ inches} $$

• A change of \(-32\text{ inches}\) means the water depth has decreased by \(32\text{ inches}\).

Answer:

Question 1

• (A) Time varies with respect to the water depth with a rate of change of \(-2\text{ day/in}\).
• (B) The water depth varies with respect to time with a rate of change of \(-2\text{ day/in}\).
• (C) The water depth varies with respect to time with a rate of change of \(-2\text{ in/day}\). (Correct answer)
• (D) Time varies with respect to the water depth with a rate of change of \(-2\text{ in/day}\).

Question 2

The water depth has <blank>decreased</blank> by <blank>8</blank> inch(es).

Question 3

The water depth has <blank>decreased</blank> by <blank>32</blank> inch(es).