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Logistic Growth Model - Inflection Points and Concavity

Leonard Lipkin and David Smith
  1. Which solutions of

    appear to have an inflection point? Express your conjecture in terms of starting values P(0). [For your convenience, the interactive figure from Part 3 is repeated here. Recall that the vertical coordinate of the point at which you click is P(0) and the horizontal coordinate is ignored.]

  1. How is the location of the inflection point (when there is one) related to K? Record your conjecture -- you will check it in the next step.
  2. Use your helper application to compute P"(t) in terms of P(t). (Don't forget the Chain Rule.) Use the resulting formula to confirm your preceding answers.
  3. What is the significance of the inflection point in terms of population growth rate?

Leonard Lipkin and David Smith, "Logistic Growth Model - Inflection Points and Concavity," Convergence (December 2004)