A genetically engineered species of rabbit is left on an island. Each pair of rabbits produces two new pairs of rabbits at the age of 1 month and six new pairs of rabbits at the age of 2 months and every month afterward. None of the rabbits ever die or leave the island. (a) Make a table to determine how many pairs of rabbits are on the island after n months, where 0 ≤ n ≤ 5. (b) It can be shown that a recurrence relation for the number of pairs of rabbits on the island after n months is given by an = 3an-1 + 4an-2, n ≥ 2. Verify that this recurrence relation is correct by checking 0 ≤ n ≤ 5 and observing that it matches your answer to part (a) (c) Solve the recurrence relation given in part (b). (d) Find the number of rabbits on the island 2 years after the first pair is left.

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