Solved: Fibonacci Variation: A single pair of rabbits (male and female) is born at the

Chapter 5, Problem 22

(choose chapter or problem)

Fibonacci Variation: A single pair of rabbits (male and female) is born at the beginning of a year. Assume the following conditions (which are more realistic than Fibonacci’s):

(1) Rabbit pairs are not fertile during their first month of life but thereafter give birth to four new male/female pairs at the end of every month.

(2) No rabbits die.

a. Let \(r_{n}\) = the number of pairs of rabbits alive at the end of month n, for each integer n ≥ 1, and let \(r_{0} = 1\). Find a recurrence relation for \(r_{0}, r_{1}, r_{2}\), . . . .

b. Compute \(r_{0}, r_{1}, r_{2}, r_{3}, r_{4}, r_{5}, and r_{6}\).

c. How many rabbits will there be at the end of the year?

Text Transcription:

r_n

r_0 = 1

r_0, r_1, r_2

r_0, r_1, r_2, r_3, r_4, r_5, and r_6