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?
To find out the number of female rabbits in the tenth generation that will be descendants of a single rabbit in the first generation, we can set up a recursive relationship.
Let's assume that the first generation consists of only one female rabbit. In this case, the number of female rabbits in each subsequent generation can be determined as follows:
- In the second generation, the only female rabbit in the first generation gives birth to three female rabbits.
- In the third generation, each of the three female rabbits from the second generation gives birth to three female rabbits, resulting in a total of 3 x 3 = 9 female rabbits.
- In the fourth generation, each of the nine female rabbits from the third generation gives birth to three female rabbits, resulting in a total of 9 x 3 = 27 female rabbits.
- This pattern continues, with each generation having three times the number of female rabbits as the previous generation.
In general, to calculate the number of female rabbits in the nth generation, we can use the formula: (number of female rabbits in the previous generation) x 3.
Applying this formula to our problem, we can find the number of female rabbits in the tenth generation:
1st generation: 1 female rabbit
2nd generation: 1 x 3 = 3 female rabbits
3rd generation: 3 x 3 = 9 female rabbits
4th generation: 9 x 3 = 27 female rabbits
5th generation: 27 x 3 = 81 female rabbits
6th generation: 81 x 3 = 243 female rabbits
7th generation: 243 x 3 = 729 female rabbits
8th generation: 729 x 3 = 2187 female rabbits
9th generation: 2187 x 3 = 6561 female rabbits
10th generation: 6561 x 3 = 19683 female rabbits
Therefore, there will be 19,683 female rabbits in the tenth generation that are descendants of a single rabbit in the first generation.