To find the rate of change in the plane's altitude, we need to determine the change in altitude and the time taken for that change.
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Change in altitude: The plane is descending 4,000 feet, which we can consider as a negative change in altitude: \[ \Delta h = -4000 \text{ feet} \]
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Time taken: It takes the pilot 3.5 minutes to descend this altitude: \[ \Delta t = 3.5 \text{ minutes} \]
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Rate of change in altitude: The rate of change in the plane's altitude can be calculated with the formula: \[ \text{Rate of change} = \frac{\Delta h}{\Delta t} \] Substituting in the values: \[ \text{Rate of change} = \frac{-4000 \text{ feet}}{3.5 \text{ minutes}} \approx -1142.86 \text{ feet per minute} \]
So, the rate of change in the plane's altitude, to the nearest hundredth, is approximately: \[ \boxed{-1142.86} \text{ feet per minute} \]
This negative sign indicates that the plane is descending.