Calc06_5 - 6.5 Logistic Growth Model Bears 40 20 0 20 40...

Info icon This preview shows pages 1–5. Sign up to view the full content.

6.5 Logistic Growth Model Years Bears Greg Kelly, Hanford High School, Richland, Washington
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

We have used the exponential growth equation to represent population growth. 0 kt y y e = 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: dP kP dt = The constant k is called the relative growth rate . / dP dt k P =
Image of page 2
The population growth model becomes: 0 kt P P e = 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 . 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: M P M -
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

The equation then becomes: dP M P kP dt M - = Our book writes it this way: Logistics Differential Equation ( 29 dP k P M P dt M = - We can solve this differential equation to find the logistics growth model.
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '08
  • chale
  • Differential Calculus, AP, Logistic function, logistic growth model, Logistics Differential Equation

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern