Questions in Discrete Mathematics- help needed

Asked Nov 29 '19 at 11:48

Active Nov 29 '19 at 13:21

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Suppose that each male/female pair of rabbits in a farm produces two new male/female pairs of rabbits at the age of 1 month and six new male/female pairs of rabbits at the age of 2 months and every month afterward. Assume that there is only one male/female pair of rabbits at the beginning of a year. Further assume that no rabbits die in the farm. Let an be the number of male/female pair of rabbits in the farm at the end of month n.

a) Determine a recurrence relation for an and clearly justify your answer.

b) By solving the recurrence relation in a) find the number of male/female pairs of rabbits in the farm at the end of month n.

c) Prove the result in b) by strong mathematical induction.

Am I right?

edited Nov 29 '19 at 13:21

emonHR

2,650

asked Nov 29 '19 at 11:48

Ting

I got that $a_{-1}=0$, $a_0=1$ and then$$a_n=3a_{n-1}+4a_{n-2}\quad n\ge1$$$$a_n=\frac15(4^n-(-1)^n)\quad n\ge0$$ – Peter Foreman Nov 29 '19 at 11:58
@Peter Foreman For question a? – Ting Nov 29 '19 at 12:52
For parts a and b respectively. – Peter Foreman Nov 29 '19 at 12:57
How about part b and c? It looks I do it wrong – Ting Dec 06 '19 at 09:29

Questions in Discrete Mathematics- help needed

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