# What is the logistic model of population growth?

The logistic population $P \left(t\right)$ can be expressed by
$P \left(t\right) = \frac{K {P}_{0}}{{P}_{0} + \left(K - {P}_{0}\right) {e}^{- r t}}$,
where ${P}_{0}$ is an initial population, $K$ is a carrying capacity, and $r$ is a growth constant.