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Math Help - population growth model

  1. #1
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    population growth model

    Having problems with a homework problem:

    2 populations (J(t) and K(t)) of microbial species are each assumed to grow according to the euler differential equation model, with different growth parameters c and d, respectively. Suppose the populations are grown together in a beaker, and define p(t) = J(t) / (J(t) + K(t)) to be the fraction of the total population that is of species type J. Using differential equations for J and K, show that p(t) satisfies a logistic growth equation.

    any input would be helpful.

    thanks,
    charps
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  2. #2
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    coming down to the wire on this one. any help or hints would be awesome.

    charps
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  3. #3
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    Maybe you can say,
    J(t)=Ae^{st}
    K(t)=Be^{rt}

    Then, show that
    p'(t)=kp(t)
    Knowing that,
    p(t)=\frac{Ae^{st}}{Ae^{st}+Be^{rt}}
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  4. #4
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    thank you.
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