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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