A single pair (male and female) of rabbits is born at the beginning of the year. Assume the following:

1) Each pair is not fertile for their first month bet thereafter give birth to four new male/female pairs at the end of every month

2) no rabbits die

a) let be the number of pairs of rabbits alive at the end of each month n for each integer find a recurrence relation for

b) how many rabbits will there be at the end of the year

Month | Babies (in pairs) | Adults (in pairs) | total Pairs (r_{n})

1 |1 |0 |1

__________________________________________________ _______________

2 |4 |1 |5

__________________________________________________ ______________

3 |20 |5 |25

__________________________________________________ ______________

4 |100 |25 |125

__________________________________________________ _________

5 |400 |125 |525

__________________________________________________ ___________

6 |2100 |525 |2625

__________________________________________________ ___________

7 |10500 |2625 |13125

__________________________________________________ ____________

8 |52500 |13125 |65625

__________________________________________________ _____________

9 |262500 |65625 |328125

__________________________________________________ ______________

10 |1312500 |328125 |1640625

__________________________________________________ _______________

11 |6562500 |1640625 |8203125

__________________________________________________ _______________

12 |328125000 |8203125 |41015625

(sorry for the ugly table)

the recurrence relation seems to be where a = number of adults, for

is that correct?

and part b) would be 41,015,625 pairs so 82,031,250 rabbits