Discussion
Female rabbits are either juvenile or adult. Each month, each juvenile grows to adulthood and each adult female gives birth (on average) to one juvenile female. Starting with one juvenile female rabbit, how many female rabbits will there be after 10 months ?
Answer: D
There will be 89 female rabbits.
Each month, adults (A) stay and each produces one juvenile (J), and each juvenile becomes an adult. So the new adults are the old adults plus the old juveniles, and the new juveniles equal the old adults:
\[ \begin{aligned} A_{n+1} &= A_{n} + J_{n} \\ J_{n+1} &= A_{n} \end{aligned} \]
Starting with one juvenile, the totals month by month are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 for months 0 to 10, the Fibonacci sequence, because each total is the sum of the two before it. After 10 months there are 89 female rabbits.
71, 79 and 81 do not belong to the sequence; 89 is the total after exactly ten steps.
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