To calculate the average rate of change of the diver’s depth, we need to find the change in depth and divide it by the time taken for that change.
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Initial Depth: The diver was at a depth of 15 meters below the surface.
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Final Depth: She descends 10 meters lower, which means her final depth is: \[ 15 , \text{meters} + 10 , \text{meters} = 25 , \text{meters} , \text{below the surface.} \]
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Change in Depth: \[ \text{Change in Depth} = \text{Final Depth} - \text{Initial Depth} = 25 , \text{meters} - 15 , \text{meters} = 10 , \text{meters.} \]
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Time Taken: 10.1 seconds.
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Average Rate of Change: \[ \text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{10 , \text{meters}}{10.1 , \text{seconds}} \approx 0.99 , \text{meters/second.} \]
However, since the diver is going deeper, we typically treat depth below the surface as negative, meaning we could express the rate of change in terms of descent as negative. So:
\[ \text{Average Rate of Change} = -\frac{10 , \text{meters}}{10.1 , \text{seconds}} \approx -0.99 , \text{meters/second.} \]
The suitable interpretation for the average rate of change for the diver’s depth would be:
The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.