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 −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 −0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second.
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Answer 1

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

1. Initial depth: \( -15 \) meters (since it's below the surface)
2. Final depth: \( -15 - 10 = -25 \) meters (10 meters lower than -15 meters)

Now, calculate the change in depth:

\[ \Delta \text{depth} = \text{Final depth} - \text{Initial depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]

Next, we divide the change in depth by the time taken for the descent to find the average rate of change:

\[ \text{Average rate of change} = \frac{\Delta \text{depth}}{\text{time}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ meters/second} \]

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 −0.99 meters/second.