Question

The table shows the linear relationship between the elevation in feet of an airplane as it descends and the number of minutes.

Number of Minutes Elevation (ft)
2 29,000
4 26,000
7 21,000
12 14,000

What is the rate of change of the elevation of the airplane with respect to the number of minutes since the plane started its descent?

900ft
1,200ft
1,500ft
1,800ft

Answer 1

To find the rate of change of the elevation of the airplane with respect to the number of minutes, we can choose any two points from the data and calculate the change in elevation divided by the change in time.

Let's take the first and last data points:
- At 2 minutes, the elevation is 29,000 ft.
- At 12 minutes, the elevation is 14,000 ft.

The change in elevation is:

\[
\text{Change in elevation} = 14,000 \text{ ft} - 29,000 \text{ ft} = -15,000 \text{ ft}
\]

The change in time is:

\[
\text{Change in time} = 12 \text{ min} - 2 \text{ min} = 10 \text{ min}
\]

Now, we can calculate the rate of change of elevation with respect to time:

\[
\text{Rate of change} = \frac{\text{Change in elevation}}{\text{Change in time}} = \frac{-15,000 \text{ ft}}{10 \text{ min}} = -1,500 \text{ ft/min}
\]

The negative sign indicates that the elevation is decreasing, but if we are only looking for the magnitude of the rate of change, it is:

**1,500 ft/min**.

So, the answer is **1,500 ft**.