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

If the change in the depth was 0 that means the depth didn't change.

Answer 2

Your average rate of change equals total change/time. This is in contrast to instantaneous rate of change which would be how fast depth is changing right now, a day ago or time T in general. That could be nonzero at any time, but if it starts at depth D and ends at depth D then average rate = (D-D)/T= 0/T= 0