In a certain nature reserve there are two competing animal species A and B. It is observe that the number of species A equals three times the number of A last year less twice the number of species B last year. Also the number of species B is twice the number of B last year less the number of species A last year. (i) Write down a system of linear recurrences for an and bn, the numbers of each species after n years, and solve the system. (Hint: one equation is given by an+1 = 3an -- 2bn.) (ii) What are the long term prospects for each species? (Hint: these will depend on the values of ao and bo.)