The Fibonacci sequence was first discovered during a study of rabbits. If newborn rabbits become adults in one month, each pair of adult rabbits produces one pair each month, and no rabbits die, then how many pairs of rabbits would be produced after seven months? How many after twelve months?
Thanks!
@steve yes, I did. I am confused on how to complete this problem.
btw,
The Fibonacci sequence was first NOT discovered during a study of rabbits.
To determine how many pairs of rabbits would be produced after seven months and twelve months, we can use the concept of the Fibonacci sequence.
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, we can consider each month as a position in the Fibonacci sequence, starting with 1. The first month is position 1, the second month is position 2, and so on.
In this scenario, newborn rabbits become adults in one month, each pair of adult rabbits produces one pair each month, and no rabbits die. So, after the first month (position 1), we have 1 pair of adult rabbits.
To find the number of pairs of rabbits after seven months, we need to calculate the Fibonacci number at position 7. We can do this either by manually calculating each Fibonacci number or by using a formula.
Manually, we would iterate through the sequence, keeping track of the last two numbers until we reach the 7th position:
Position 1: 1 pair
Position 2: 1 pair
Position 3: 2 pairs (1 + 1)
Position 4: 3 pairs (2 + 1)
Position 5: 5 pairs (3 + 2)
Position 6: 8 pairs (5 + 3)
Position 7: 13 pairs (8 + 5)
Therefore, after seven months, there would be 13 pairs of rabbits.
Similarly, to calculate the number of pairs after twelve months, we can either manually calculate up to the 12th position or use a formula. Using the formula for the Fibonacci sequence, we can calculate it as follows:
Fibonacci(12) = Fibonacci(11) + Fibonacci(10)
= (Fibonacci(10) + Fibonacci(9)) + (Fibonacci(9) + Fibonacci(8))
= (Fibonacci(9) + Fibonacci(8)) + (Fibonacci(8) + Fibonacci(7))
= ... (continue this process until position 1 and position 2)
After calculating each term, we find that the Fibonacci number at position 12 is 144.
Therefore, after twelve months, there would be 144 pairs of rabbits.
so, did you actually read about the Fibonacci sequence?
The F.S. tells you how many pairs there will be after n months. The sequence is
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
So, what is the 7th term? the 12th?