For the recurrence $a_n = 1.05a_{n-1} - 0.05a_{n-2},$ the characteristic equation $r^2 - 1.05r + 0.05 = 0$ has roots $r_1 = 1$ and $r_2 = 0.05$.

Given that the general solution is $a_n = c_1 \cdot 1^n + c_2 \cdot 0.05^n$ with $c_1 \neq 0$, what best describes the long-term behavior?