Logistic vs. Exponential Growth Models

This GeoGebra example dynamically compares exponential growth and logistic growth models. It demonstrates how an exponential curve rises indefinitely, while a logistic curve approaches a carrying capacity, forming an S-shaped (sigmoid) trajectory. The core mathematical concepts include differential equations, exponential functions, the logistic equation, limits, asymptotes, and the effect of parameters on curve shape. Construction details: The example uses the Point command to create key points (r, r_1, A, B, C, etc.), sliders or parameters to control growth rate r and carrying capacity y(A), and the FormulaText command to dynamically display the logistic equation y' = r*y*(1 - y/K) as text. It also includes scatter plots and multiple curves (green for the logistic solution, others for exponential or comparison). This resource is suitable for high school to university-level teaching, especially in calculus, differential equations, or mathematical biology courses to explore population growth models and resource limitations.