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Unit 7 Test Tuesday Feb 11th

Unit 7 Test Tuesday Feb 11th. AP #2 Friday Feb 7 th Computer Lab (room 253) Monday Feb 10 th HW: p. 357 #23-26 , 31, 38, 41, 42. Exponential growth is unlimited growth. M = Carrying capacity is the maximum population size that an environment can support.

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Unit 7 Test Tuesday Feb 11th

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  1. Unit 7 TestTuesday Feb 11th AP #2 Friday Feb 7th Computer Lab (room 253) Monday Feb 10th HW: p. 357 #23-26, 31, 38, 41, 42

  2. Exponential growth is unlimited growth. M = Carrying capacity is the maximum population size that an environment can support Logistic growth is slowed by population-limiting factors

  3. We have used the exponential growth equation to represent population growth. The exponential growth equation occurs when the rate of growth is proportional to the amount present. If we use P to represent the population, the differential equation becomes: The constant k is called the relative growth rate.

  4. The population growth model becomes: A more realistic model is the logistic growth model where growth rate is proportional to both the amount present (P) and the fraction of the carrying capacity that remains: However, real-life populations do not increase forever. There is some limiting factor such as food, living space or waste disposal. There is a maximum population, or carrying capacity, M.

  5. Logistic Differential Equation The equation then becomes: Our book writes it this way: We can solve this differential equation to find the logistic growth model.

  6. Partial Fractions Logistic Differential Equation

  7. Logistic Differential Equation

  8. Logistic Growth Model

  9. Logistic Growth Model Bears Years

  10. Example: Logistic Growth Model Ten grizzly bears were introduced to a national park 10 years ago. There are 23 bears in the park at the present time. The park can support a maximum of 100 bears. Assuming a logistic growth model, when will the bear population reach 50? 75? 100?

  11. Ten grizzly bears were introduced to a national park 10 years ago. There are 23 bears in the park at the present time. The park can support a maximum of 100 bears. Assuming a logistic growth model, when will the bear population reach 50? 75? 100?

  12. At time zero, the population is 10.

  13. After 10 years, the population is 23.

  14. Bears Years We can graph this equation and use “trace” to find the solutions. y=50 at 22 years y=75 at 33 years y=100 at 75 years

  15. Logistic Growth diff eq  solution

  16. If you are told Logistic Growth you can go directly from diff eq to Carrying Capacity Population “Room to grow” constant rate time

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