A bacterial colony's population $P_n$ at generation $n$ follows: $P_n = 2P_{n-1} - 0.8P_{n-2}$

where $P_0 = 100$ and $P_1 = 180$. The characteristic roots are $r_1 = 2$ and $r_2 = -0.4$.

For large $n$, which term dominates the population, and why?