Logistic Growth Model

Part 3: Inflection Points and Concavity

1. Which solutions of

   

   appear to have an inflection point? Express your answer in terms of starting values P(0). [For your convenience, the interactive figure from Part 2 is repeated here. Recall that the vertical coordinate of the point at which you click is P(0) and the horizontal coordinate is ignored.]

2. How is the location of the inflection point (when there is one) related to K?

3. Use your helper application to compute P" in terms of P. (Don't forget the Chain Rule.) Use the resulting formula to confirm your preceding answers.

4. What is the significance of the inflection point in terms of population growth rate?

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