Question 19.34

4. Here are two primitive models of natural increase of biological populations, similar to those that Fibonacci hypothesized around the year 1200, based on the following situation: A pair of newborn male and female rabbits is placed in an enclosure to breed.

  1. Suppose that the rabbits start to bear young one month after their own birth. At the end of each month, they have another male-female pair, which in turn mature and start to bear young one month later. Assuming that none of the rabbits die, how many pairs of rabbits will there be at the end of six months from the start (just before any births for that month)? (Hint: Draw a month-by-month chart of the situation at the end of the month, just before any births.)
  2. Repeat part (a), but assume instead that the rabbits start to bear young exactly two months after their own birth.