To find the rate of change of the altitude of the airplane with respect to time, we can calculate the change in altitude over the change in time between the given points.
Using the values from the table:
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From 1.5 minutes to 3.25 minutes:
- Change in altitude = 24000 feet - 28000 feet = -4000 feet
- Change in time = 3.25 minutes - 1.5 minutes = 1.75 minutes
- Rate of change = Change in altitude / Change in time
- Rate of change = -4000 feet / 1.75 minutes ≈ -2285.71 feet per minute
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From 3.25 minutes to 6 minutes:
- Change in altitude = 19000 feet - 24000 feet = -5000 feet
- Change in time = 6 minutes - 3.25 minutes = 2.75 minutes
- Rate of change = Change in altitude / Change in time
- Rate of change = -5000 feet / 2.75 minutes ≈ -1818.18 feet per minute
Both calculations show negative values, indicating that the altitude is decreasing.
To summarize:
- The rate of change of the altitude of the airplane is approximately -2286 feet per minute (during the first interval) and -1818 feet per minute (during the second interval), indicating that the altitude is decreasing at a constant rate. If more precise values or an exact constant rate across the intervals is needed, it may require determining a linear equation based on all points combined to find a single overall rate.
For the overall change from 1.5 to 6 minutes:
- Total change in altitude = 19000 feet - 28000 feet = -9000 feet
- Total change in time = 6 minutes - 1.5 minutes = 4.5 minutes
- Overall rate of change = -9000 feet / 4.5 minutes = -2000 feet per minute
Thus, the overall average rate of change of the altitude of the airplane is -2000 feet per minute.
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