Biological exponential growth

[1] Most commonly apparent in species that reproduce quickly and asexually, like bacteria, exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.

[3][4] Resources are the determining factor in establishing biological exponential growth, and there are different mathematical equations used to analyze and quantify it.

[1][2] Ideally, when resources in the habitat are unlimited, each species can fully realize its innate potential to grow in number, as Charles Darwin observed while developing his theory of natural selection.

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 theoretically reach an enormous population if there were unlimited resources for its growth in its habitat.

[4] One equation used to analyze biological exponential growth uses the birth and death rates in a population.

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

[6] Once the carrying capacity, or K, is incorporated to account for the finite resources that a population will be competing for within an environment, the aforementioned equation becomes the following:

[6] A graph of this equation creates an S-shaped curve, which demonstrates how initial population growth is exponential due to the abundance of resources and lack of competition.