Mathematical Modeling of Population Growth: A Comparative Study of Exponential Model

Abstract-Population growth is a multifaceted and evolving issue that has captivated the attention of demographers, ecologists, and policymakers for many years. The swift increase in the global population carries significant consequences for resource management, environmental sustainability, and socioeconomic development. This study seeks to enhance the current body of knowledge on population growth by creating and comparing mathematical models that reflect the fundamental dynamics of this phenomenon. In particular, this research examines the exponential and logistic models of population growth, which are commonly utilized in the fields of demography and ecology. The exponential model posits that population growth is influenced by a constant birth rate and death rate, whereas the logistic model considers the environmental carrying capacity and the effects of resource constraints on population growth. Employing a mix of analytical and numerical techniques, this study evaluates the advantages and drawbacks of each model in forecasting population growth across various scenarios. The findings underscore the necessity of accounting for environmental carrying capacity and resource limitations when modeling population growth, and illustrate how mathematical models can guide policy and decision making in areas such as demography, ecology, and resource management. The implications of this study are significant for our comprehension of population growth and its effects on both the environment and society. The outcomes can be leveraged to create more precise and realistic population models, which can aid in policy and decision-making at local, national, and global scales. Additionally, this research showcases the potential of mathematical modeling to deepen our understanding of intricate social and environmental issues, emphasizing the need for further exploration in this area.