Question

A whale is swimming at a current depth of 15 meters below the surface. It swims up toward the surface and arrives there 9.5 seconds later. Find the quotient that best describes the rate of change in the whale’s depth. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the whale’s depth is
meters/second.
Remaining Attempts : 3

Answer 1

To find the rate of change in the whale's depth, we need to determine how much the depth changes and how long it takes for that change to occur.

The whale starts at a depth of 15 meters below the surface, which we can represent as -15 meters (since "below the surface" is negative in this context).

When the whale reaches the surface, its depth is 0 meters. The change in depth can be calculated as:

\[
\text{Change in depth} = \text{Final depth} - \text{Initial depth} = 0 - (-15) = 15 \text{ meters}
\]

Now, we divide this change in depth by the time taken to find the rate of change:

\[
\text{Rate of change} = \frac{\text{Change in depth}}{\text{Time}} = \frac{15 \text{ meters}}{9.5 \text{ seconds}} \approx 1.578947368 \text{ meters/second}
\]

Rounding this to the nearest hundredth gives:

\[
\text{Rate of change} \approx 1.58 \text{ meters/second}
\]

So, the quotient that best describes the rate of change in the whale’s depth is \( \boxed{1.58} \) meters/second.