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.

Answer 1

"The pool must have been the same depth at the start of the interval as it was at the end of the interval" is the statement among the choices given in the question that must be true. The correct option among all the options that are given in the question is the second option. I hope the answer has helped you.

Answer 2

Answer: The pool must have been the same depth at the start of the interval as it was at the end of the interval.

Step-by-step explanation:

The average rate of change is calculated as:

[final value - initial value] / time interval.

Then, the average rate of change does not take into account intermediates values, and you cannot draw any conclusion about such intermediate values.

In the given case you have:

average rate of change in depth = [final depth - initial depth] / 2 weeks.

0 = [final depth - initial depth] / 2 weeks.

⇒ 0 = final depth - initial depth

⇒ final depth = initial depth.

That is why the conclusion is the second statement of the answer choices: the pool must have been the same depth at the start of the interval as it was at the end of the interval.

In between the pool might have been deeper, more shallow, empty or change in any form, since the average rate of change does not tell the full history but only the net change.