# More Looney Math

Algebra Level 5

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

$\begin{eqnarray} r(t+1)&=&0.8r(t)-0.7c(t)+200 \\ c(t+1)&=&0.7r(t)+0.8c(t)-170 \end{eqnarray}$

If there are 310 roadrunners and 200 coyotes initially (at time $$t=0$$), find $$\displaystyle \lim_{t\to\infty}(r(t)^2+c(t)^2)$$ according to this model.

If you come to the conclusion that no such (finite) limit exists, enter 666.

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