From the exponential to the logistic equation: how the carrying capacity K of the environment turns unchecked growth into a sigmoidal curve. A standalone R Markdown lesson with qualitative analysis, phase portrait, numerical solution (deSolve) and parameter estimation.
How, starting from a simple observation — a 10% daily increase in the water lilies of a lake — we arrive at the exponential growth formula by way of a differential equation. A standalone R Markdown lesson with text, R code, plots and mathematics.
