scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. she made the descent in 10.1 seconds. interpret the quotient to describe the rate of change in the diver’s depth. give your answer to the nearest hundredth.(1 point) responses a. the quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second. b. the quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second. c. the quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second. d. the quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.

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.**