# 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. Population growth in which the number of individuals increase by a constant multiple in each generation. The potential for population growth can be demonstrated in the laboratory under conditions that provide abundant resources and space. For example, a few fruit flies in a large culture jar containing an abundant food source may reproduce rapidly. One female fruit fly may lay more than 50 eggs. Reproductive adults develop in about 14 days, with approximately equal numbers of male and female offspring. For each female that began the population, 50 flies are expected 2 weeks later. Each female in the second generation produces 50 more flies after 2 more weeks, and so on. In other words, the population is experiencing exponential growth.[1] Slow exponential growth is when a population grows slowly yet exponential because the population has long live spans. While a rapid exponential growth refers to a population that grows ( and dies ) rapidly because the population has short life spans.

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:

${\displaystyle dN/dt=(b-d)N}$

(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.