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Help with logistic growth problem

  1. Jan 27, 2014 #1
    Hi all, I've got this logistic growth problem that I'm unsure of on how to start. I missed a day of class and don't have a chance to go to office hours, so any help would be much appreciated.

    I've been given a set of values: time, population, and change in population.

    The values are as follows, with each value correlation to each time value of course:
    T=0.0, P=2.0, dP/dt=0.11
    T=37.71, P=14.0, dP/dt=0.62
    T=45.05, P=19.0, dP/dt=0.74
    T=57.45, P=29.0, dP/dt=0.84

    I've been asked to predict population, P at T=10.

    A point in the right direction would be great, thanks.
     
  2. jcsd
  3. Jan 28, 2014 #2

    pasmith

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    Homework Helper

    The ODE you are trying to solve is
    [tex]
    \frac{dP}{dt} = kP(P_0 - P)
    [/tex]
    for some constants [itex]k[/itex] and [itex]P_0[/itex] which you can estimate from the given data for [itex]dP/dt[/itex] and [itex]P[/itex].
     
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