Question

A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excess turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane's altitude. Give your answer to the nearest hundredth, and remember the plain is descending. The quotient that best represents the rate of change in the plane's altitude is:

Answer 1

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.

1. Change in altitude: The plane is descending 4,000 feet, which we can consider as a negative change in altitude: \[ \Delta h = -4000 \text{ feet} \]

2. Time taken: It takes the pilot 3.5 minutes to descend this altitude: \[ \Delta t = 3.5 \text{ minutes} \]

3. 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.