How many rabbits will be born?

[ExtremeSi]

Hey, I just got this homework question on my first day at class and I don't have the text book yet so I was hoping someone on here could help me solve it. There's got to be some sort of formula.

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on.
How many pairs will there be in one year?

Any help would be appreciated! Thanks very much

 

[stapel]

Start working with the numbers, and see if you can come up with a pattern. At zero months (t = 0), how many rabbits are there? How many are females that are mating? At one month (t = 1), how many rabbits are there? How many are females that are mating? At two months (t = 2), how many rabbits are there? How many are females that are mating? How many are having kittens?

And so forth, until you "see" the pattern. Have fun!

Eliz.

 

[ExtremeSi]

Wow this is really not getting to me. I've drawn diagrams, listed numbers and I just can't wrap my brain around it. I keep getting lost with what rabbits can mate and which ones can't.
So far I have:

Month Rabbits FemalesMating
0 0 0
1 2 1
2 4 1
3 6 2
4 10 2

Is this right at all? I can't keep track. Thanks for the help

 

[Deleted member 4993]

Wow this is really not getting to me. I've drawn diagrams, listed numbers and I just can't wrap my brain around it. I keep getting lost with what rabbits can mate and which ones can't.
So far I have:

Month Rabbits FemalesMating
0 0 0
1 2 1
2 4 1
3 6 2
4 10 2

Is this right at all? I can't keep track. Thanks for the help

Have you studied Fibonacii (sp?) Sequence?

In there, every term is created by summation of two terms before it. thus it goes

1,1,2,3,5,8,13,21,34.....

Do you see similarity between your problem and one such sequence?

The sequence can start with any two given nubers - for example:

2, 4, 6, 10, 16, 26, ... etc.

Anyway, the problem as presented is not a probability/statistics problem. In stead, it is an arithmatric problem.