# Biological exponential growth

Biological exponential growth is the exponential growth of biological organisms. When the resources availability is unlimited in the habitat, the population of an organism living in the habitat grows in an exponential or geometric fashion.

Resource availability is obviously essential for the unimpeded growth of a population. Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number, as Charles Darwin observed while developing his theory of natural selection.

If, in a hypothetical population of size N, the birth rates (per capita) are represented as b and death rates (per capita) as d, then the increase or decrease in N during a time period t will be:

$dN/dt=(b-d)N$

(b-d) is called the 'intrinsic rate of natural increase' and is a very important parameter chosen for assessing the impacts of any biotic or abiotic factor on population growth.

Any species growing exponentially under unlimited resource conditions can reach enormous population densities in a short time. Darwin showed how even a slow growing animal like the elephant could reach an enormous population if there were unlimited resources for its growth in its habitat.

If birth giving takes two parents we get Nurgaliev's law.