Recurrence relation

• May 6th 2007, 09:50 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?

• May 6th 2007, 11:15 PM
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?