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

Answer 1

To find the average rate of change of the diver's depth, we first need to determine the total change in depth and then divide this change by the time taken for the descent.

1. Initial Depth: The diver starts at 15 meters below the surface, which can be expressed as -15 meters.

2. Final Depth: The diver descends to a depth of 10 meters lower than this initial position. So, the final depth is:

   \[ -15 \text{ meters} - 10 \text{ meters} = -25 \text{ meters} \]

3. Change in Depth: The change in depth is calculated as:

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

4. Time Taken: The time taken for this change is 10.1 seconds.

5. Average Rate of Change: The average rate of change of the diver's depth can be calculated using the formula:

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

Rounding this to the nearest hundredth, the average rate of change is approximately:

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

So, the correct interpretation of the average rate of change for the diver’s depth is:

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