Growth and Decay of an Entity’s Population: A Differential Calculus Approach

Abstract

In this research report, it is the study of the growth or decay of a population according to the resources. Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, ie when the resources are unlimited, a population P believes according to the following differential equation P' = KP, with the application of the differential calculus we obtain an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment ie when resources are limited, the population can not exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P' = P(1 - P).