The Use of Differential Equations in Studying Population Growth

Abstract

Population growth is an important concept in biology, ecology, economics, and demography because it dictates the manner in which resources are utilized, urbanism, and environmental policies. This paper is a discussion on the application of the use of differential equations in the modeling of population growth. Two of them are analyzed, the exponential growth model, which presupposes unlimited resources, and the logistic growth model, which presupposes environmental restrictions by the carrying capacity. The findings indicate that the exponential model is more appropriate to describe an accelerated population growth in a perfect situation, whereas the logistic model is more realistic in terms of the long-term prognosis because it takes into consideration resource limitations. The paper emphasizes the role of the differential equations in the prediction of the population trends, resource planning, and ecological dynamics. Policy, education and research recommendations are also addressed.