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:

`d/(dt)2000\ ln(t+1)=2000/(t+1)`

At *t* = 3, we have *v* = 2000/4 = 500 feet/min.

So the required rate of climb is 500'/min.

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