Worksheet: The Logistic Model

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In this worksheet, we will practice using logistic population growth models.

Q1:

Suppose a population grows according to a logistic model with a carrying capacity of 7 500 and 𝑘 = 0 . 0 0 6 . Write the logistic differential equation for this information.

  • A d d 𝑃 𝑡 = 𝑃 0 . 0 0 6 − 𝑃 7 5 0 0
  • B d d 𝑃 𝑡 = 0 . 0 0 6 𝑃 1 + 𝑃 7 5 0 0
  • C d d 𝑃 𝑡 = 0 . 0 0 6 1 − 𝑃 7 5 0 0
  • D d d 𝑃 𝑡 = 0 . 0 0 6 𝑃 1 − 𝑃 7 5 0 0
  • E d d 𝑃 𝑡 = 𝑃 0 . 0 0 6 + 𝑃 7 5 0 0

Q2:

Suppose a population grows according to a logistic model with a carrying capacity of 2 500 and 𝑘 = 0 . 0 0 4 . Write the logistic differential equation for this information.

  • A d d 𝑃 𝑡 = 𝑃 0 . 0 0 4 − 𝑃 2 5 0 0
  • B d d 𝑃 𝑡 = 0 . 0 0 4 𝑃 1 + 𝑃 2 5 0 0
  • C d d 𝑃 𝑡 = 0 . 0 0 4 1 − 𝑃 2 5 0 0
  • D d d 𝑃 𝑡 = 0 . 0 0 4 𝑃 1 − 𝑃 2 5 0 0
  • E d d 𝑃 𝑡 = 𝑃 0 . 0 0 4 + 𝑃 2 5 0 0

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