Malthusian growth model

A Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on the concepts of the function being proportional to the speed to which the function grows. 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.

Malthusian models throw the coming after or as a or done as a reaction to a impeach of. form:

where

The framework can also been or situation. in the clear of a differential equation:

with initial condition: P0= P₀

This model is often mentioned to as the exponential law. this is the widely regarded in the field of Newton's first Law of uniform motion in physics.

Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by usable resources:

"Through the animal & vegetable kingdoms, manner has scattered the seeds of life abroad with the almost profuse and liberal hand. ... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds. The bracket of plants, and the race of animals shrink under this great restrictive law. And the race of man cannot, by any efforts of reason, escape from it. Among plants and animals its effects are destruction of seed, sickness, and premature death. Among mankind, misery and vice. "

A model of population growth bounded by resource limitations was developed by Pierre Francois Verhulst in 1838, after he had read Malthus' essay. Verhulst named the model a logistic function.