To find the rate of change of the elevation of the airplane with respect to time (which is the slope), we can calculate the rise over run using the elevation and time data.
We have the following points from the table:
- (2, 1200)
- (4, 3600)
- (7, 7200)
- (12, 13200)
We can calculate the slope between two points, or we can find the overall rate of change.
Let's take the first and last points for a more comprehensive calculation:
- For the first point (2 minutes, 1200 ft) and the last point (12 minutes, 13200 ft):
\[ \text{Slope} = \frac{\text{Change in elevation}}{\text{Change in time}} = \frac{13200 - 1200}{12 - 2} \]
Calculating the change in elevation:
\[ 13200 - 1200 = 12000 \text{ ft} \]
Calculating the change in time:
\[ 12 - 2 = 10 \text{ minutes} \]
Now we can find the rate of change (slope):
\[ \text{Slope} = \frac{12000 \text{ ft}}{10 \text{ min}} = 1200 \text{ ft/min} \]
Thus, the rate of change of the elevation of the airplane with respect to the number of minutes is:
b) 1200 ft/min.