# Beep, Beep!

A stretch of desert is populated by two species of animals, roadrunners and coyotes, who are engaged in an endless game of rivalry and mischief. The populations $$r(t)$$ and $$c(t)$$ of roadrunners and coyotes $$t$$ years from now can be modelled by

$\begin{eqnarray} r(t+1)&=&3r(t)-2c(t) \\ c(t+1)&=&5r(t)-3c(t)-100 \end{eqnarray}$

If there are 120 roadrunners and 110 coyotes initially (at time $$t=0$$), how many roadrunners will there be 1001 years later (at time $$t=1001$$)?

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