Grabbits are genetically modified rabbits that live forever and reproduce asexua

Question

Grabbits are genetically modified rabbits that live forever and reproduce asexually on a precise schedule: each grabbit gives birth to three grabbits every Wednesday starting two weeks after birth. So if you start with 1 newly born grabbit, after one week you will still only have 1 grabbit. After two weeks you will have 4 grabbits, namely your first grabbit plus its 3 offspring. In general, how many grabbits will you have after n weeks if you start with one newly born grabbit? Set up a recurrence relation for this problem and solve it. Recurrence relation: Characteristic polynomial and its roots: General form of the solution: Initial condition equations and their solution: Final answer:

Explanation / Answer

for (a) the recurrence is Rn= R(n-1)+3*R(n-2).

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