The graph of h = 2000 ln (t + 1) shows that it is a realistic model for the climb performance of a light aircraft. At low altitudes, where the air is more dense, the rate of climb is good, but as you go higher, the rate decreases.
[For some background on graphing logarithm functions, see Graphs of Exponential and Logarithmic Functions.]
To find the rate of climb (vertical velocity), we need to find the first derivative:
At t = 3, we have v = 2000/4 = 500 feet/min.
So the required rate of climb is 500'/min.
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