Question

A 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 The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second. The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second. The quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second. The quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second. The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second. The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second. The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.

Answer 1

To find the average rate of change in the diver's depth, we need to determine the change in depth and the time taken for that change.

1. **Initial depth**: The diver starts at 15 meters below the surface, which is -15 meters in terms of depth.
2. **Final depth**: The diver descends to a depth of 10 meters lower than her initial depth. Therefore, her final depth is:
\[
-15 \text{ meters} - 10 \text{ meters} = -25 \text{ meters}
\]

3. **Change in depth**: The change in depth \( \Delta d \) is:
\[
\Delta d = \text{final depth} - \text{initial depth} = -25 \text{ meters} - (-15 \text{ meters}) = -25 + 15 = -10 \text{ meters}
\]

4. **Time taken**: The time for the descent was 10.1 seconds.

5. **Average rate of change (quotient)**: Now we can calculate the average rate of change using the formula:
\[
\text{Average Rate of Change} = \frac{\Delta d}{\Delta t} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ meters/second}
\]

Rounding this to the nearest hundredth gives us:
\[
\text{Average Rate of Change} \approx -0.99 \text{ meters/second}
\]

Thus, the correct interpretation is:
The quotient that describes the average rate of change for the diver’s depth is **−0.99 meters/second**.