A population of bacteria follows $\mathbf{x}_{n+1} = A\mathbf{x}_n$ where $A = \begin{pmatrix} 0.8 & 0.3 \\ 0.2 & 0.7 \end{pmatrix}$. The eigenvalues are $\lambda_1 = 1$ and $\lambda_2 = 0.5$. For large $n$, the population distribution approaches a steady state proportional to the eigenvector of $\lambda = 1$. If $\mathbf{v}_1 = \begin{pmatrix} 3 \\ 2 \end{pmatrix}$ is the eigenvector for $\lambda_1 = 1$, what is the long-term ratio of the two species?