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?
a increase
b decrease
time, x (minutes): 1.5, 3.25, 6
altitude, y (feet): 28000, 24500, 19000
what is it at the rate of?
a 1,000 feet per minute
b 2,000 feet per minute
c 3,000 feet per minute
d 4,000 feet per minute

Answer 1

To determine the rate of change of altitude with respect to time, we first need to calculate the change in altitude and the change in time from the data provided in the table.

Let's pick two points from the table for the calculation:

• Point 1: (3.25, 24500)
• Point 2: (6, 19000)

Now, we calculate the change in altitude (y) and the change in time (x):

1. Change in altitude: \[ \Delta y = y_2 - y_1 = 19000 - 24500 = -5500 \text{ feet} \]

2. Change in time: \[ \Delta x = x_2 - x_1 = 6 - 3.25 = 2.75 \text{ minutes} \]

Now, we can find the rate of change of altitude: \[ \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{-5500 \text{ feet}}{2.75 \text{ minutes}} \approx -2000 \text{ feet per minute} \]

The negative sign indicates that the altitude is decreasing.

Thus, the completed statements are:

• The altitude of the airplane DECREASES.
• The rate of change is approximately 2,000 feet per minute.

So the answers are:

• The altitude of the airplane: b decrease
• The rate of change: b 2,000 feet per minute