Logistic Equation

Used to solve first-order non-linear models the logistic differential equation takes the form:

Referred to as the general logistic equation, is population. The equation builds on the first-order linear model. The logistic equation's solution is:

The derivation of the above solution can be found in W2L3 - Non-linear Models.

An alternate form and solution is as follows (provided by Video 2 - The Logistic Equation and the Analytic Solution):

is max population capacity.