# Recurrence relation

• May 6th 2007, 10:50 PM
smoothi963
Recurrence relation
A single pair of rabbits (male and female) is born at the beginning of a year and placed alone on a small island.

Assume these conditions:
(i) Rabbit pairs are not fertile during their first month of life, but thereafter give birth to four new male/female.
(II) no rabbits die

A. Let An = the number of pairs of rabbits alive at the end of the month n, for each integer n >= 1 and let Ao = 1. Find a recurrence relation for this situation.

B. How many rabbits will thre be at the end of the year?

C. How many rabbits will there be after 10years?

Thank you in advance.
• May 7th 2007, 12:15 AM
Glaysher
Quote:

Originally Posted by smoothi963
A single pair of rabbits (male and female) is born at the beginning of a year and placed alone on a small island.

Assume these conditions:
(i) Rabbit pairs are not fertile during their first month of life, but thereafter give birth to four new male/female.
(II) no rabbits die

A. Let An = the number of pairs of rabbits alive at the end of the month n, for each integer n >= 1m and let Ao = 1. Find a recurrence relation for this situation.

B. How many rabbits will thre be at the end of the year?

C. How many rabbits will there be after 10years?

Thank you in advance.

a) An+1 = 3An, A1 = 2

b) 2 x 3^11

c) 2 x 3^119
• May 7th 2007, 12:18 AM
smoothi963
Thanks glaysher, would it be too much trouble to ask you to tell me how you got to the answer. Thank you