Fitting P(t) to the 1950-1990 Data: A Plan

In order to fit the logistic function to the data, we have to determine the unknown parameters . But we also have three equations:

So, it makes sense to proceed as follows. From the data, we will let be the recorded population in 1950; will be the population in the year when the growth rate is a maximum; and will be the maximum growth rate. Once we have these numbers on the left-hand-sides, we then will attempt to solve the resulting three equations in three unknowns. This indeed is a workable plan.

Now, to obtain these numbers, we need only to determine the maximum growth rate. As in the past, we will use the average of the right and left estimates of the derivative to develop a table of growth rates and proceed from there. Does all of this seem reasonable?