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 in the altitude of the airplane with respect to time.
does the altitude of the airplane INCREASE or DECREASE?
time, x (minutes): 1.5, 3.25, 6
altitude, y (feet): 28000, 24500, 19000
what is it at the rate of?

Answer 1

To determine the rate of change in the altitude of the airplane with respect to time, we can calculate the change in altitude over the change in time using the data provided.

Let's look at the points given in the table:

1. At \( x = 1.5 \) minutes, \( y = 28000 \) feet.
2. At \( x = 3.25 \) minutes, \( y = 24500 \) feet.
3. At \( x = 6 \) minutes, \( y = 19000 \) feet.

Next, we can calculate the changes in altitude and time:

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

   • Change in altitude: \( 24500 - 28000 = -3500 \) feet
   • Change in time: \( 3.25 - 1.5 = 1.75 \) minutes
   • Rate of change: \( \frac{-3500}{1.75} = -2000 \) feet per minute

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

   • Change in altitude: \( 19000 - 24500 = -5500 \) feet
   • Change in time: \( 6 - 3.25 = 2.75 \) minutes
   • Rate of change: \( \frac{-5500}{2.75} = -2000 \) feet per minute

Since both calculations give us a rate of change of \(-2000\) feet per minute, we can conclude the following:

The altitude of the airplane DECREASES at a rate of 2000 feet per minute.