Question

You buy an island and stock it with 1000 rabbits. There is no emigration or immigration to the island and the rabbits die at a rate of 120 per year. What is the maximum number of new daughters that can be born each year on average and still have the population shrink?

Answer 1

Total number of rabbit on the island = 1000

The number of rabbit dying each other = 120

Now, assume that the number of daughters born each year is equal to the number of rabbit dying i.e., 120. In this case, the population will remain the same (1000-120+120) = 1000

The maximum number of daughters born each years should be one less than half the number of death each year, i.,e, (60-1) = 59. At this number of births of daughter, the population of rabbit dying each year would be (120-59) = 61, i.e., more than half their original number. Therefore, the population would shrink.

So, the answer is 59.