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

Answer 1

To calculate the average rate of change of the diver’s depth, we need to find the change in depth and divide it by the time taken for that change.

1. **Initial Depth**: The diver was at a depth of 15 meters below the surface.
2. **Final Depth**: She descends 10 meters lower, which means her final depth is:
\[
15 \, \text{meters} + 10 \, \text{meters} = 25 \, \text{meters} \, \text{below the surface.}
\]

3. **Change in Depth**:
\[
\text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = 25 \, \text{meters} - 15 \, \text{meters} = 10 \, \text{meters.}
\]

4. **Time Taken**: 10.1 seconds.

5. **Average Rate of Change**:
\[
\text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{10 \, \text{meters}}{10.1 \, \text{seconds}} \approx 0.99 \, \text{meters/second.}
\]

However, since the diver is going deeper, we typically treat depth below the surface as negative, meaning we could express the rate of change in terms of descent as negative. So:

\[
\text{Average Rate of Change} = -\frac{10 \, \text{meters}}{10.1 \, \text{seconds}} \approx -0.99 \, \text{meters/second.}
\]

The suitable interpretation for the average rate of change for the diver’s depth would be:

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