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.
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Initial depth: 15 meters below the surface (this is -15 meters).
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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).
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Change in depth: \[ \text{Change in depth} = \text{Final depth} - \text{Initial depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]
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Time taken: 10.1 seconds.
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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.