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Homework Help: Logistic Equation Calculus Question

  1. Feb 11, 2007 #1
    1. The problem statement, all variables and given/known data

    Suppose that a population develops according to the logistic equation
    dp/dt = 0.03 p - 0.006 p^2
    where t is measured in weeks.
    -What is the carrying capacity and the value of k?

    2. Relevant equations

    dp/dt = kP ( 1 - (p/K)) where K is the carrying capacity

    3. The attempt at a solution

    Well i thought that in order to solve this i need to get the differenctial expression give in the question to resemble that of the logistic equation so i can get the values. so far my attempts have failed...so i dont know if THAT is wat i am actually supposed to do.
    I rearranged the equation and i got:
    dp/dt = P^2 ( (o.o3/P) - 0.oo6)
    = 0.006 P^2 ( (5/P) - 1)
    = -0.006 P^2 ( 1- (5/P))
    that is the farthest I went so far i dont really know wat to do next or whether or not I am understanding this question correctly. Any help would be greatly appreciated :smile:
  2. jcsd
  3. Feb 22, 2007 #2
    You have the general form, but then you factored out a p^2. Now you are inventing another form....

    To paraphrase "Only Euclid has seen beauty bare" .... but not here.
  4. Feb 22, 2007 #3


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    Staff Emeritus
    Science Advisor

    So, you want to get your equation in the form [tex]\frac{dp}{dt}=\frac{rp(K-p)}{K}=rp(1-\frac{p}{K})[/tex], where here r is the Malthusian parameter (your k) and K is the carrying capacity.

    Your mistake was factoring out p2, since this gives us a term which looks like 1/p instead of p inside the brackets. You should do this: [tex]\frac{dp}{dt}=0.006p(5-p)=0.03p(1-\frac{p}{5})[/tex]. Can you solve now?
    Last edited: Feb 22, 2007
  5. Feb 22, 2007 #4
    thanks for the help i got the right answer :biggrin:
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