Question

lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. which statement must be true?

• the pool must have been empty for the entire interval.
• the pool must have been the same depth at the start of the interval as it was at the end of the interval.
• the pool must have been deeper at the end of the interval than it was at the start of the interval.
• the pool must have been more shallow at the end of the interval than it was at the start of the interval.

Explanation:

Define average rate of change formula

$$ \text{Average Rate of Change} = \frac{d(t_2) - d(t_1)}{t_2 - t_1} $$

Set average rate of change to zero and solve

$$
LATEXBLOCK0
$$

Match result with the given statements

$$ d(t_{\text{start}}) = d(t_{\text{end}}) $$

Answer:

• The pool must have been empty for the entire interval.
• The pool must have been the same depth at the start of the interval as it was at the end of the interval. (Correct answer)
• The pool must have been deeper at the end of the interval than it was at the start of the interval.
• The pool must have been more shallow at the end of the interval than it was at the start of the interval.