Logistic Growth (BC)

AP Calculus · Axiom Academy

Modeling populations with a carrying capacity Real populations can t grow forever. The logistic model adds a carrying capacity L that limits growth. Logistic Differential Equation When P is small, growth is nearly exponential ( ) Growth rate is maximum at P = L/2 (the inflection point) As , (population approaches carrying capacity) The S-shaped curve is called a sigmoid or logistic curve Logistic: ; solution is a sigmoid Maximum growth rate occurs at P = L/2 Equilibria at P = 0 (unstable) and P = L (stable) BC-only topic, frequently tested

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