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 solve this problem, we need to understand the population growth pattern of the rabbits. According to the given information, each female rabbit gives birth to three female rabbits.
Let's break down the generations:
First generation: 1 rabbit (starting point)
Second generation: 1 rabbit gives birth to 3, so we have a total of 1 + 3 = 4 rabbits.
Third generation: Each rabbit from the second generation gives birth to 3, so we have a total of 4 + (3 * 3) = 13 rabbits.
Fourth generation: Each rabbit from the third generation gives birth to 3, so we have a total of 13 + (3 * 13) = 52 rabbits.
Fifth generation: Each rabbit from the fourth generation gives birth to 3, so we have a total of 52 + (3 * 52) = 208 rabbits.
Sixth generation: Each rabbit from the fifth generation gives birth to 3, so we have a total of 208 + (3 * 208) = 832 rabbits.
Seventh generation: Each rabbit from the sixth generation gives birth to 3, so we have a total of 832 + (3 * 832) = 3328 rabbits.
Eighth generation: Each rabbit from the seventh generation gives birth to 3, so we have a total of 3328 + (3 * 3328) = 13312 rabbits.
Ninth generation: Each rabbit from the eighth generation gives birth to 3, so we have a total of 13312 + (3 * 13312) = 53248 rabbits.
Tenth generation: Each rabbit from the ninth generation gives birth to 3, so we have a total of 53248 + (3 * 53248) = 212992 rabbits.
Therefore, we have 212,992 female rabbits of the tenth generation who are descendants of a single rabbit from the first generation.