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 Write-up

Title
Multiplying Rabbits

Problem Statement
A newly born rabbit is capable of reproducing at one month old (when it matures). Suppose the rabbit never dies, and it continues reproducing one new rabbit every month. So, when the rabbit is born, it has one member in its own family. After a month, it matures, and by the second month it adds a new born member to its family. In the third month, the rabbit produces another offspring; its first child also matures and will be ready to have an offspring in the next month.

The sequence named by Fibonacci (1,1,2,3,5,8,13,21,...) can describe the number of members in the rabbit's family at each month. Explain how.

Problem setup

This problem is asking you to figure out the number of rabbits there will be each month given the reproduction pattern.

Plans to Solve/Investigate the Problem

In order to figure out how many there will be in any given month, I analyzed the Fibonacci sequence.  After looking at it, you have to add the number of rabbits at the beginning of the last two months and that will be the number of rabbits at the beginning of the next month.

Investigation/Exploration of the Problem

Below is a portion of the spread sheet that I created that illustrates what I did to solve this  problem.

 # of months # of rabbits 1 1 2 1 3 2 4 3 5 5 6 8 7 13 8 21 9 34

The first column illustrates the number of months and the second represents the number of rabbits in that month that I got from the Fibonacci sequence.

Benjamin Moore

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Link(s) to resources, references, lesson plans, and/or other materials

Fibonacci Numbers and the Golden Section -
This page discuss applications, real world phenomena, puzzles, patterns, and geometry associated with the Fibonacci numbers and golden section.

Fibonacci Number -- From MathWorld
Fibonacci Number -- from MathWorld