Diagonalization & Matrix Powers · Medium problem

Let $\mathbf{x}(t)$ solve $\mathbf{x}' = A\mathbf{x}$ with $A = \begin{pmatrix}-3 & 1\\2 & -2\end{pmatrix}$ and $\mathbf{x}(0) = \begin{pmatrix}2\\1\end{pmatrix}$. Find $\displaystyle\lim_{t\to\infty}\dfrac{x_2(t)}{x_1(t)}$.