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 −0.99 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.

Answer 1

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

1. **Starting depth**: 15 meters below the surface = -15 meters (considering below the surface as negative)
2. **Depth she descended to**: 10 meters lower than her starting depth
- New depth = -15 - 10 = -25 meters.
3. **Change in depth**: New depth - Initial depth = -25 - (-15) = -25 + 15 = -10 meters.
4. **Time taken for the descent**: 10.1 seconds.

Now, we can 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 get:

\[
-0.99 \text{ meters/second}.
\]

Therefore, the correct interpretation is:

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