Section Summary

In this section we derived symbolic representations for solutions of the logistic growth differential equation:

In the process we developed a new approach to finding antiderivatives — an approach that uses the technique of rewriting quotients of polynomials as sums of simpler quotients. One form of our symbolic solution,

exhibits again the role of negative exponentials in expressions that approach a limiting value as `t` becomes large.

We also saw that we could use an intermediate step in the separation-of-variables solution,

1 M ⁢ ln ⁢ P M - P ⁢ = k ⁢ t + C ,

to test whether data fit a logistic growth pattern.