BM-862302/Pgrowth-Modelling

Modeling of population growth in Cape Coast, Ghana using 4exponential differential equations, historical census data and numerical projections. Originally an undergraduate research project; open for further development. # Population Growth Modeling of Cape Coast, Ghana ## Overview This repository contains an undergraduate applied mathematics research project focused on modeling the population growth of Cape Coast, Ghana. The study applies the exponential growth model to historical census data in order to estimate growth rates and project future population trends. The project aims to demonstrate how mathematical modeling can support demographic analysis, urban planning, and sustainable development decision-making. ## Objectives The main objectives of this project are: - To understand and apply exponential growth models in population dynamics - To estimate the population growth rate of Cape Coast using census data - To project future population sizes based on mathematical modeling - To discuss the implications of population growth for urban planning and resource allocation ## Methodology The project uses the exponential growth model defined by the equation: \[ P(t) = P_0 e^{rt} \] where: - \( P(t) \) is the population at time \( t \) - \( P_0 \) is the initial population - \( r \) is the constant growth rate - \( t \) represents time in years Historical population data were obtained from the Ghana Statistical Service (GSS) census reports. The growth rate was estimated using logarithmic regression, and future population projections were generated assuming a constant growth rate. ## Data Sources - Ghana Statistical Service Population and Housing Census Reports (1960–2021) - Academic literature on population growth and mathematical demography ## Tools and Technologies - Python (for computation and visualization) - Microsoft Excel (data handling and preliminary analysis) - Mathematical analysis using differential equations --- ## Key Findings - Cape Coast has experienced steady population growth over the past six decades. - The estimated annual growth rate between 2010 and 2021 is approximately **1.01%**. - Under the exponential growth assumption, the population is pro …