Application of First-Order Differential Equations to Population Growth Models

Mathematics — 2025, Undergraduate

This study applied first-order differential equations to the modelling of population growth. Exponential and logistic models were formulated, solved, and calibrated to observed growth data, and qualitative behaviour was interpreted. The findings revealed that the logistic model described growth with limiting capacity more realistically than the exponential model at longer horizons. The study observed that parameter estimation strongly influenced predictions. It recommends calibrated differential-equation models for population and resource planning.

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