Question

A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months? See illustration, top right.

   A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months? See illustration, top right.

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 11, Problem 85

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We start with one pair of mature rabbits. Each pair of mature rabbits produces a new pair of offspring each month. The offspring take one month to mature, and then they can reproduce starting from the second month after their birth. Show more…

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A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months? See illustration, top right.

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Key Concepts

Fibonacci Sequence

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. It often appears in nature, particularly in scenarios modeling idealized reproductive patterns. In many introductory mathematics problems, such as idealized population growth or breeding problems, the sequence naturally arises as an elegant solution to a recurrence relation with simple initial conditions.

Recurrence Relations

A recurrence relation is a mathematical equation that defines a sequence recursively: each term is formulated based on previous terms. This approach is widely used in modeling dynamic systems, such as populations where the number of individuals at a given time depends on past generations. In problems of population growth in biology or finance, setting up a recurrence relation helps predict future behavior based on current and historical data.

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