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Logistic Growth

Logistic Growth. Logistics Differential Equation. L. L = Carrying Capacity Limit as . Ex. 1 The population of fish in a lake satisfies the logistic differential equation , where t is measured in years, and .

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Logistic Growth

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  1. Logistic Growth

  2. Logistics Differential Equation L L = Carrying Capacity Limit as

  3. Ex. 1 The population of fish in a lake satisfies the logistic differential equation , where t is measured in years, and . (a) (b) What is the range of the solution curve? (c) For what values of P is the solution curve increasing? Decreasing? Justify your answer.

  4. (c) For what values of P is the solution curve increasing? Decreasing? Justify your answer. (d) For what values of P is the solution curve concave up? Concave down? Justify your answer. (e) Does the solution curve have an inflection point? Justify your answer.

  5. Ex. 2 The population of fish in a lake satisfies the logistic differential equation , where t is measured in years, and P(0) = 10,000 . (a) (b) What is the range of the solution curve? (c) For what values of P is the solution curve increasing? Decreasing? Justify your answer.

  6. (d) For what values of P is the solution curve concave up? Concave down? Justify your answer. (e) Does the solution curve have an inflection point? Justify your answer.

  7. Ex. 3 The population of fish in a lake satisfies the logistic differential equation , where t is measured in years, and . (a) (b) What is the range of the solution curve? (c) For what values of P is the solution curve increasing? Decreasing? Justify your answer.

  8. For what values of P is the solution curve concave up? Concave down? Justify your answer. (e) Does the solution curve have an inflection point? Justify your answer.

  9. Tonight’s homework: Worksheet

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