Question

To find the rate of change in the whale's depth, we can use the formula for rate of change, which is:

\[
\text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}}
\]

1. **Determine the change in depth**:
- The whale starts at a depth of 15 meters (which is below the surface, so we can use -15 meters).
- It swims up to the surface, which is 0 meters.
- Therefore, the change in depth is:

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

2. **Determine the time**:
- The time taken for this change is 9.5 seconds.

3. **Calculate the rate of change**:
\[
\text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{15 \text{ meters}}{9.5 \text{ seconds}}
\]

Now we compute the quotient:

\[
\text{Rate of Change} = \frac{15}{9.5} \approx 1.5789
\]

4. **Round to the nearest hundredth**:
\[
1.5789 \approx 1.58
\]

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