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    The Malthusian and Logistic Models of Population Growth

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    Please see the attached file. This is one question but broken in parts.

    Formula for Malthusian Model:
    dP/dt = r*P

    Formula for Logistic Model:

    PS> I Prefer hand written work showing the steps if it is neat. It's up to you..I just have a hard time reading fractions & exponents in a word document etc.

    (ie. (3/5)^2.

    © BrainMass Inc. brainmass.com May 20, 2020, 9:01 pm ad1c9bdddf


    Solution Preview

    See the attached file.


    Let P (t) represent a population of farm-raised catfish in a small lake at any
    time t in days.

    (a) If the population grows according to the Malthusian model, find the time for the
    catfish population to triple if it grows by 10% in 45 days. Show all of you work.
    Your answer should be exact (it will contain logarithms)

    According to the Malthusian model, we have
    dP/dt = r*P
    for some constant r. Separating variables we obtain
    dP/P = r dt.
    Integrating both sides we obtain
    ln P(t) = rt + c
    for some constant c. Exponentiating both sides we ...

    Solution Summary

    The solution solves problems involving catfish breeding assuming either the Malthusian model (unlimited exponential growth) or the more realistic logistic model of population growth.