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Worksheet: The Logistic Model

Q1:

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

  • A d d 𝑃 𝑑 = 𝑃 ο€Ό 0 . 0 0 4 βˆ’ 𝑃 2 5 0 0 
  • B d d 𝑃 𝑑 = 0 . 0 0 4 𝑃 ο€Ό 1 + 𝑃 2 5 0 0 
  • C d d 𝑃 𝑑 = 0 . 0 0 4 ο€Ό 1 βˆ’ 𝑃 2 5 0 0 
  • D d d 𝑃 𝑑 = 0 . 0 0 4 𝑃 ο€Ό 1 βˆ’ 𝑃 2 5 0 0 
  • E d d 𝑃 𝑑 = 𝑃 ο€Ό 0 . 0 0 4 + 𝑃 2 5 0 0 

Q2:

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

  • A d d 𝑃 𝑑 = 𝑃 ο€Ό 0 . 0 0 6 βˆ’ 𝑃 7 5 0 0 
  • B d d 𝑃 𝑑 = 0 . 0 0 6 𝑃 ο€Ό 1 + 𝑃 7 5 0 0 
  • C d d 𝑃 𝑑 = 0 . 0 0 6 ο€Ό 1 βˆ’ 𝑃 7 5 0 0 
  • D d d 𝑃 𝑑 = 0 . 0 0 6 𝑃 ο€Ό 1 βˆ’ 𝑃 7 5 0 0 
  • E d d 𝑃 𝑑 = 𝑃 ο€Ό 0 . 0 0 6 + 𝑃 7 5 0 0 