📝Practice Screen #5.

Question

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

Number of Minutes
Elevation (ft)
2
1,200
4
3,600
7
7,200
12
13,200
What is the rate of change of the elevation of the airplane with respect to the number of minutes since the plane started its ascent?

Remember that rate of change is slope.

Answer 1

To find the rate of change of elevation with respect to time, we can use the formula for slope:

\[ \text{slope} (m) = \frac{\text{change in elevation}}{\text{change in time}} = \frac{\Delta y}{\Delta x} \]

In this case, \(y\) represents the elevation in feet, and \(x\) represents the number of minutes. We will use two points from the table to calculate the slope. Let's use the points (2, 1200) and (12, 13200).

1. Identify the change in elevation: \[ \Delta y = 13200 - 1200 = 12000 \text{ ft} \]

2. Identify the change in time: \[ \Delta x = 12 - 2 = 10 \text{ minutes} \]

3. Calculate the slope: \[ m = \frac{\Delta y}{\Delta x} = \frac{12000}{10} = 1200 \text{ ft/min} \]

Therefore, the rate of change of the elevation of the airplane with respect to the number of minutes is 1200 feet per minute.