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.

Answer 1

To find the rate of change in the whale's depth as it swims up to the surface, we first need to determine the total change in depth and the time taken.

The whale starts at a depth of 15 meters below the surface and swims up to the surface (0 meters). So, the change in depth is:

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

The time taken for this change is 9.5 seconds.

Now we can calculate the rate of change in depth (which is the quotient):

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

Calculating this gives:

\[
\text{Rate of change} \approx \frac{15}{9.5} \approx 1.57894736842
\]

Rounding this to the nearest hundredth:

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

Thus, the quotient that best represents the rate of change in the whale’s depth is **1.58 meters/second**.