To find the average rate of change in the diver's depth, we first need to determine the change in depth and the time taken.
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Initial Depth: The diver was at a depth of 15 meters below the surface, so we can represent this as -15 meters.
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Final Depth: The diver descends to a depth that is 10 meters lower than -15 meters, which means she reaches a depth of -15 - 10 = -25 meters.
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Change in Depth: This is the final depth minus the initial depth: \[ \text{Change in Depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]
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Time Taken: The time taken for this descent is 10.1 seconds.
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Average Rate of Change: The average rate of change in depth is calculated by dividing the change in depth by the time taken: \[ \text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time Taken}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.99 \text{ meters/second} \]
Thus, the quotient that describes the average rate of change for the diver’s depth is approximately -0.99 meters/second.
The correct interpretation is: The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
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