How many pairs of rabbits will there be after a year if it is assumed that
every month each pair produces one new pair, which begins to bear two young two months after its
own birth?
How many pairs do you have to start?
we have 1 pair start with
To determine the number of pairs of rabbits after a year, we can use the concept of Fibonacci sequence.
In this scenario, each pair of rabbits produces one new pair each month, and this new pair starts to reproduce two months after its birth.
Let's break it down step by step:
Month 1: We start with one pair of rabbits.
Month 2: The initial pair reproduces and gives birth to a new pair.
Month 3: Both the initial pair and the one born in the previous month are still too young to reproduce.
Month 4: The initial pair produces another pair, while the first-born pair is now old enough to reproduce.
Month 5: The initial pair reproduces again, while the first-born pair is still the only one able to reproduce.
Month 6: The initial pair produces another pair, the first-born pair reproduces for the first time, and now we have three pairs.
Month 7: The initial pair reproduces once more, the first-born pair reproduces again, and we have five pairs in total.
Month 8: The initial pair reproduces, the first-born pair reproduces again, and we have a total of eight pairs.
.
.
.
And so on.
We can see that the pattern here follows the Fibonacci sequence. Each month, the number of pairs of rabbits is the sum of the previous two months. Thus, the sequence goes like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.
For a year, we need to calculate up to the 12th month. Using the Fibonacci sequence, the 12th month will give us the number of pairs of rabbits after a year.
Therefore, there will be 144 pairs of rabbits after a year based on this assumption.