I am posting this question in Biology instead of Algebra even though it is a question from my Algebra class. Thanks.
A male bee has only one parent(a mother) and a female bee has two parents (a mother and a father).Assuming all ancestors are distinct, how many great, great, great, great grandparents does a male bee have?
To determine the number of great, great, great, great grandparents a male bee has, we need to track the ancestors for each generation.
1. The male bee has one mother.
2. In the next generation, the male bee's mother will have two parents (a grandmother and a grandfather).
3. Going back another generation, the male bee's grandmother and grandfather would each have two parents, resulting in four great-grandparents.
4. In the following generation, the great-grandparents would each have two parents, resulting in eight great-great-grandparents.
5. Going back one more generation, the great-great-grandparents would each have two parents, resulting in sixteen great, great, great grandparents.
Therefore, a male bee has 16 great, great, great, great grandparents.
To determine the number of great, great, great, great grandparents a male bee has, we need to understand the concept of generations and the inheritance pattern.
Each "great" qualifier represents one generation. So, one "great" means one generation back. In this case, we are going back four generations: great, great, great, great grandparents.
Since a male bee has only one parent (a mother), we can assume that it is a result of asexual reproduction, such as parthenogenesis. This means that the male bee does not have a father.
For the female bee, who needs both a mother and a father, we can assume sexual reproduction.
In each generation, a male bee has only one parent, while a female bee has two parents. Therefore, for every generation going back, the number of ancestors doubles for the females.
Let's calculate the number of great, great, great, great grandparents for a female bee:
- Great grandparents: 2 parents
- Great, great grandparents: 2 x 2 = 4 grandparents
- Great, great, great grandparents: 2 x 2 x 2 = 8 great, great grandparents
- Great, great, great, great grandparents: 2 x 2 x 2 x 2 = 16 great, great, great, great grandparents
Since a male bee has only one parent and does not have a father, we can conclude that a male bee has zero great, great, great, great grandparents in the typical sense.
So, to summarize:
- A female bee has 16 great, great, great, great grandparents.
- A male bee has zero great, great, great, great grandparents.