Verhulst-Pearl logistic growth is expressed by:
$\frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)$
where $N =$ population density at time $t$
$K =$ the maximum number of organisms that can be supported by a habitat without environmental degradation is called carrying capacity
$r =$ the number of birth rates minus the number of death rates in a population is called the intrinsic rate of natural increase.