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 minutesComplete the statement that describes the rate of change of the altitude of the airplane with respect to time.

Question

Time,X(minutes)
1.5,3.25,6
Altitude,y(feet)
28,000, 24,500, 19,000

Answer 1

To analyze the rate of change of altitude with respect to time, we can calculate the change in altitude over the change in time between the points provided in the table.

Let's determine the altitude change between the first two points and then between the second and third points.

1. From \(x = 1.5\) minutes to \(x = 3.25\) minutes:

   • Change in altitude: \(28,000 - 24,500 = 3,500\) feet
   • Change in time: \(3.25 - 1.5 = 1.75\) minutes
   • Rate of change: \(\frac{3,500 \text{ feet}}{1.75 \text{ minutes}} = 2,000 \text{ feet per minute}\)

2. From \(x = 3.25\) minutes to \(x = 6\) minutes:

   • Change in altitude: \(24,500 - 19,000 = 5,500\) feet
   • Change in time: \(6 - 3.25 = 2.75\) minutes
   • Rate of change: \(\frac{5,500 \text{ feet}}{2.75 \text{ minutes}} \approx 2,000 \text{ feet per minute}\)

Since the rate of change is consistent in both cases, we conclude that the altitude of the airplane is decreasing at a constant rate of approximately 2,000 feet per minute.

Complete Statement

The rate of change of the altitude of the airplane with respect to time is a decrease of approximately 2,000 feet per minute.