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Math Help - Recurrence relation

  1. #1
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    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.
    Last edited by smoothi963; May 6th 2007 at 11:21 PM.
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  2. #2
    Member Glaysher's Avatar
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    Quote Originally Posted by smoothi963 View Post
    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
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  3. #3
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    Thanks glaysher, would it be too much trouble to ask you to tell me how you got to the answer. Thank you
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