The altitude of an airplane is changing at a constant rate. The table shows the linear relationship between `y`, the altitude of the airplane in feet, and `x`, the time in minutes.

Question

Complete the statement that describes the rate of change of the altitude of the airplane with respect to time.
Time, x (minutes):1.5, 3.25, 6
Altitude, y (feet): 28000, 24000,19000

Answer 1

To describe the rate of change of the altitude of the airplane with respect to time, we can calculate the change in altitude (y) over the change in time (x) between the points given in the table.

1. From the first point (1.5 minutes, 28000 feet) to the second point (3.25 minutes, 24000 feet):

   • Change in altitude: 24000 - 28000 = -4000 feet
   • Change in time: 3.25 - 1.5 = 1.75 minutes
   • Rate of change: \(\frac{-4000 \text{ feet}}{1.75 \text{ minutes}} \approx -2285.71 \text{ feet/minute}\)

2. From the second point (3.25 minutes, 24000 feet) to the third point (6 minutes, 19000 feet):

   • Change in altitude: 19000 - 24000 = -5000 feet
   • Change in time: 6 - 3.25 = 2.75 minutes
   • Rate of change: \(\frac{-5000 \text{ feet}}{2.75 \text{ minutes}} \approx -1818.18 \text{ feet/minute}\)

It appears the altitude is decreasing over time. Since the rate of change is approximately consistent, we can conclude that the airplane is descending at a constant rate.

To complete the statement:

"The altitude of the airplane is decreasing at an average rate of approximately -2285.71 feet per minute with respect to time."

or,

"The airplane descends at a constant rate of approximately 2286 feet per minute."

Both statements convey that the altitude is decreasing.