# Malthusian growth model

A Malthusian Growth Model, sometimes called a simple exponential growth model, is essentially exponential growth based on a constant rate. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on population.[1]

Malthusian models have the following form:

$P(t) = P_0e^{rt} \,$

where

• P0 = P(0) is the initial population size,
• r = the population growth rate, sometimes called Malthusian parameter,
• t = time.

This model is often referred to as the exponential law.[2] It is widely regarded in the field of population ecology as the first principle of population dynamics,[3] with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law.[4]

It is generally acknowledged that populations can not grow indefinitely. [5] Joel E. Cohen has stated that the simplicity of the model makes it useful for short-term predictions, but not of much use for predictions beyond 10 or 20 years.[6]

The simplest way to limit Malthusian growth model is by extending it to a logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' essay.