Math Help - Gompertz growth

1. 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!

2. Originally Posted by brogers
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