The table shows the linear relationship between the elevation in feet of an airplane as it descends and the number of minutes.
number of minutes
2
4
7
12
elevation (ft)
29,000
26,000
21,500
14,000
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?
To find the rate of change of the elevation of the airplane with respect to the number of minutes, we can use the formula for the slope of a line, which is given by:
slope = (change in elevation) / (change in minutes)
To calculate the change in elevation, we subtract the initial elevation from the final elevation:
change in elevation = 14,000 ft - 29,000 ft = -15,000 ft
To calculate the change in minutes, we subtract the initial number of minutes from the final number of minutes:
change in minutes = 12 min - 2 min = 10 min
Now we can calculate the slope:
slope = (change in elevation) / (change in minutes) = -15,000 ft / 10 min = -1500 ft/min
Therefore, the rate of change of the elevation of the airplane with respect to the number of minutes is -1500 ft/min.