The graph of h = 2000 ln (t + 1) shows that it is a realistic model for the climb performance of an aircraft. At low altitudes, where the air is more dense, the rate of climb is good, but as you go higher, the rate decreases.

climb out

[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 ln

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

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