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)

Question

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 negative 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 −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 −0.49 meters/second.

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 (this is -15 meters).

2. Final depth: 10 meters lower than her initial depth means she descends to a depth of 25 meters below the surface (which is -25 meters).

3. Change in depth: \[ \text{Change in depth} = \text{Final depth} - \text{Initial depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]

4. Time taken: 10.1 seconds.

5. Average rate of change: \[ \text{Average rate of change} = \frac{\text{Change in depth}}{\text{Time}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ meters/second} \]

Rounding to the nearest hundredth, we find that the average rate of change for the diver's depth is approximately −0.99 meters/second.

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