Malthusian growth model

A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea 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 have the following form:
where
The model can also been written in the form of a differential equation:
with initial condition:
P(0)= P0
This model is often referred to as the "exponential law". It is widely regarded in the field of population ecology as the first principle of population dynamics, with Malthus as the founder. The exponential law is therefore also sometimes referred to as the "Malthusian Law". By now, it is a widely accepted view to analogize Malthusian growth in Ecology to 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 available resources:
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.