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. Complete the statement that describe the rate of change of the altitude of the airplane with respect to time.

Question

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

____ at a rate of: 1,000 feet per minute, 2,000 feet per minute, 3,000 feet per minute, or 4,000 feet per minute.

_____ The altitude of the airplane: decreases or increases?

Answer 1

To understand the rate of change of the altitude of the airplane, we can calculate the change in altitude over the change in time using the values from the table.

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

   • Change in time: \( 3.25 - 1.5 = 1.75 \) minutes
   • Change in altitude: \( 24,500 - 28,000 = -3,500 \) feet
   • 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 time: \( 6 - 3.25 = 2.75 \) minutes
   • Change in altitude: \( 19,000 - 24,500 = -5,500 \) feet
   • Rate of change: \( \frac{-5,500 \text{ feet}}{2.75 \text{ minutes}} = -2,000 \text{ feet per minute} \)

In both intervals, the rate of change is consistent:

• The altitude of the airplane decreases at a rate of 2,000 feet per minute.

Now, completing the statements: The airplane's altitude decreases at a rate of: 2,000 feet per minute.

The altitude of the airplane: decreases.