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Math Help - Gompertz growth

  1. #1
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    Gompertz growth

    I am given \frac{dN}{dt}=\gamma N where \frac{d\gamma}{dt}=-\alpha \gamma

    How do I get \frac{dN}{dt}=\gamma_{0}e^{-\alpha t}N if I know \frac{1}{N}\frac{dN}{dt}=\frac{d}{dt}(ln (N))?
    Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by brogers View Post
    I am given \frac{dN}{dt}=\gamma N where \frac{d\gamma}{dt}=-\alpha \gamma

    How do I get \frac{dN}{dt}=\gamma_{0}e^{-\alpha t}N if I know \frac{1}{N}\frac{dN}{dt}=\frac{d}{dt}(ln (N))?
    Thanks!
    Just solve:

    \frac{d\gamma}{dt}=-\alpha \gamma

    for \gamma and substitute back into the original equation.

    CB
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