# Beep, Beep!

**Discrete Mathematics**Level 4

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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