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 −0.49 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.

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/sec

Answer 1

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

1. **Initial depth**: 15 meters below the surface (which we can represent as -15 meters).
2. **Final depth**: 10 meters lower than this, which is -15 - 10 = -25 meters.
3. **Change in depth**: Final depth - Initial depth = -25 - (-15) = -25 + 15 = -10 meters.
4. **Time taken for descent**: 10.1 seconds.

Now, we can calculate the average rate of change:

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

So, the correct interpretation is:

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