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.

900 ft/min

1,200ft/min

1,500 ft/min

1,800 ft/min

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 using the formula:

\[ \text{slope} = \frac{\text{change in elevation}}{\text{change in time}} \]

We can choose two points from the table for this calculation. Let's use the first and last points:

• At 2 minutes, the elevation is 1,200 ft.
• At 12 minutes, the elevation is 13,200 ft.

Now, calculate the change in elevation and the change in time:

\[ \text{Change in elevation} = 13,200 - 1,200 = 12,000 \text{ ft} \]

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

Now substitute these values into the slope formula:

\[ \text{slope} = \frac{12,000 \text{ ft}}{10 \text{ min}} = 1,200 \text{ ft/min} \]

Thus, the rate of change of the elevation of the airplane with respect to the number of minutes is

\[ \boxed{1,200 \text{ ft/min}}. \]