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 0.99 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 −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.

Answer 1

To determine the average rate of change of the diver's depth, we first need to calculate the initial and final depths, and then find the change in depth over the change in time.

1. Initial Depth: The diver is at a depth of 15 meters below the surface.

2. Final Depth: The diver descends to a depth that is 10 meters lower than the initial depth. Therefore:

   • Final Depth = Initial Depth + 10 meters = 15 meters + 10 meters = 25 meters below the surface.

3. Change in Depth:

   • Change in Depth = Final Depth - Initial Depth = 25 meters - 15 meters = 10 meters.

4. Time Taken: The divers’ descent takes 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 this to the nearest hundredth, the average rate of change of the diver’s depth is approximately 0.99 meters/second.

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