A car rental company has three locations in Mexico City: the International Airport, Oficina Vallejo, and Downtown. Customers can drop off their vehicles at any of these locations. Based on prior experience, the company expects that, at the end of each day, $40\%$ of the cars that begin the day at the Airport will end up Downtown, $50\%$ will return to the Airport, and $10\%$ will be at Oficina Vallejo. Similarly, $70\%$ of the Oficina Vallejo cars will end up Downtown, with $10\%$ returning to Oficina Vallejo and $20\%$ to the Airport. Finally, $30\%$ of Downtown cars will end up at each of the other locations, with $40\%$ staying at the Downtown location.

This scenario can also be investigated using a discrete$-$time population model.

Consider a system of three equations $($as in Example $6\mathrm{.}23)$ giving An$,$ Vn$,$ and Dn each as functions of An $1,$ Vn $1,$ and Dn $1.$ Suppose that, initially,

A$0=1000,$

V$0=0,$

and

D$0=0.$

Use your system to compute A$2,$ V$2,$ and D$2.$