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 negative 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 0.99 meters/second.
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Answer 1

To find the average rate of change of the diver's depth, we can first determine the change in depth and then divide that by the time taken.

1. **Initial Depth**: 15 meters below the surface
2. **Final Depth**: 15 + 10 = 25 meters below the surface (since she descends 10 meters lower)

The change in depth:

\[
\text{Change in depth} = \text{Final Depth} - \text{Initial Depth} = -25 - (-15) = -10 \text{ meters}
\]

We take the change in depth as negative because the diver is going deeper below the surface.

3. **Time taken**: 10.1 seconds

Now we calculate the average rate of change of depth:

\[
\text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ meters/second}
\]

Rounding to the nearest hundredth, we have:

\[
\text{Average Rate of Change} \approx -0.99 \text{ meters/second}
\]

So, the correct interpretation of the quotient is:

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