Differential Calculus the Study of the Growth and Decay of an Entity’s Population

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, i.e. 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 obtasin 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 i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

Existence of Exactly n+1 Simple 4-Periodic Solutions of the Differential Delay Equation x(t)=-f(x(t-1))

By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).