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

Question

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 the elevation of the airplane with respect to the number of minutes, we can calculate the slope of the line formed by the given points (number of minutes vs. elevation in feet).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

We can choose two points from the table to calculate the slope. Let's take the first and the last points:

1. For \( (2, 1200) \) (2 minutes, 1200 feet)
2. For \( (12, 13200) \) (12 minutes, 13200 feet)

Now we can plug these values into the slope formula:

\[ m = \frac{13200 - 1200}{12 - 2} = \frac{12000}{10} = 1200 \]

Thus, the rate of change of the elevation of the airplane is 1200 feet per minute.