9.4: Models for Population Growth. Logistic Model.

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Presentation transcript:

9.4: Models for Population Growth

Logistic Model

Equilibrium Solutions

Slope Fields for Logistic Models Draw a slope field for the logistic equation with k = 0.08 and carrying capacity M = 1000.

Slope Fields for Logistic Models

Solution Curves

Solution to Logistic Equations

Inflection Points

Logistic Equations

b)A slope field is shown. Where are the slopes close to 0? Where are they largest? Which solutions are increasing? Which solutions are decreasing?

Logistic Equations c)Use the direction field to sketch solutions for initial populations 20, 40, 60, 80, 120, and 140. What do these have in common? How do they differ? Which solutions have inflection points? At what population levels do they occur?