Assume that each female rabbit of a colony gives birth to three female rabbits. How many female rabbits of the tenth generation will be descendants of a singal rabbit of the first generation?

Answer 1

consider if each gave birth to only 1. Then the descendants would be

1,1,1,1,1,1,1...1
Nn = n

If two, then
1,2,4,8...
Nn = 2^(n-1)

If three, then
1,3,9,27,81,243,...
Nn = 3^(n-1)

So, what's 3^9?