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?

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?

To find the number of female rabbits in the tenth generation that are descendants of a single rabbit in the first generation, we need to determine the pattern and use it to calculate the total.

From the given information, it states that each female rabbit gives birth to three female rabbits. This means that each rabbit in the next generation has three offspring. We can represent this as a recursive formula:

R(n) = 3 * R(n-1)

Where R(n) represents the number of rabbits in the nth generation, and R(n-1) represents the number of rabbits in the previous generation.

To solve this recursively, we start with the first generation. Let's assume there is only one female rabbit in the first generation:

R(1) = 1

Now we can calculate the number of rabbits in each subsequent generation:

R(2) = 3 * R(1) = 3 * 1 = 3
R(3) = 3 * R(2) = 3 * 3 = 9
R(4) = 3 * R(3) = 3 * 9 = 27
...
R(10) = 3 * R(9)

Now we can use the formula to calculate the number of rabbits in the tenth generation:

R(10) = 3 * R(9)
= 3 * (3 * R(8))
= 3 * (3 * (3 * R(7)))
= 3 * (3 * (3 * (3 * R(6))))
...
= 3^9 * R(1)
= 3^9

Therefore, there would be 3^9 (or 19683) female rabbits in the tenth generation that are descendants of a single rabbit in the first generation.