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Differential Equations Problem, logistic models

  1. Feb 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Given that a population, P, after t months, can be modeled by the logistic model
    dP/dt = .3 P (3.5 - P/40).
    P(0) = 30

    a) Solve the diff eq

    b) Find the population after 2.5 months

    c) Find lim P(t) as t -> infinity

    2. Relevant equations

    P(t) = P0 P1 /(P0 + (P1 - P0 )e^(-AP1 t))

    A = k3 /2
    P1 = (2k1 / k3 ) +1

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 23, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    hi, beccajd
    You have pretty much done part a) already. You have written down the correct solution. So now you can work out what k1 and k3 should be, by looking at the numbers in the equation given to you. I think this is everything they expect from part a). Try doing part b), it shouldn't be too difficult, since you have got the equation for it.
     
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