To find the average rate of change in the diver's depth, we first need to determine the change in depth and the time taken for that change.
1. **Initial Depth**: 15 meters below the surface (which we take as -15 meters).
2. **Final Depth**: 10 meters lower than her initial depth means she descended to \( -15 - 10 = -25 \) meters.
3. **Change in Depth**: The change in depth is:
\[
\text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = (-25) - (-15) = -10 \text{ meters}
\]
4. **Time Taken**: The time taken to descend is 10.1 seconds.
To find the average rate of change of depth, we use the formula:
\[
\text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time Taken}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}}
\]
Calculating this, we get:
\[
\text{Average Rate of Change} \approx -0.9901 \text{ meters/second}
\]
When rounding to the nearest hundredth, it becomes:
\[
-0.99 \text{ meters/second}
\]
Therefore, the correct response is:
**a. the quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.**