(a) A rabbit breeder has one male-female pair of newborn rabbits. After reaching two months of age, these rabbits and their offspring breed two other male-female pairs each month. Write a recurrence relation and initial conditions for rn, the number of pairs of rabbits after n months. Assume that no rabbits die during the n months. (b) Show that the recurrence relation in (a) satisfies r = 2rn-1 + (-1)" for n ≥ 2, and find a formula expressing In as a function of n.

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