The table shows the linear relationship between the elevation in feet of an airplane as it descends and the number of minutes.
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?
Number of Minutes
Elevation (ft)
2
29,000
4
26,000
7
21,500
12
14,000
900 ft/min
1,200 ft/min
• 1,500 ft/min
1,800 ft/min
To find the rate of change of the elevation of the airplane with respect to the number of minutes, you can calculate the difference in elevation between two consecutive minutes and divide it by the difference in the number of minutes.
For example, to find the rate of change between 2 minutes and 4 minutes:
Difference in elevation = 26,000 ft - 29,000 ft = -3,000 ft
Difference in minutes = 4 minutes - 2 minutes = 2 minutes
Rate of change = Difference in elevation / Difference in minutes
Rate of change = -3,000 ft / 2 minutes
Rate of change = -1,500 ft/min
Similarly, you can calculate the rate of change for the other sets of data:
Rate of change between 4 minutes and 7 minutes = (21,500 ft - 26,000 ft) / (7 minutes - 4 minutes) = -1,500 ft/min
Rate of change between 7 minutes and 12 minutes = (14,000 ft - 21,500 ft) / (12 minutes - 7 minutes) = -1,800 ft/min
Therefore, the rate of change of the elevation of the airplane with respect to the number of minutes since the plane started its descent is 1,500 ft/min.