The equilibria of this model are $x_n=0$ and $x_n= 5 \ln{\left (3 \right )}$. The function $g(x)=3 x e^{- \frac{x}{5}}$ and the diagonal are plotted below.

Calculate the equilibria of the dynamical system and their stability. If the initial population is $m_0=500$, what will happen to the population after a long time?