Question

We say that the animal's eight great-grandparents are "three generations back" from the animal. At which generation back would an animal have 262,144 ancestors?

Answer 1

An animal would have 262,144 ancestors 18 generations back. By using logarithms, we can find that n equals 18 when 2^n is equal to 262,144.

Step-by-step explanation:

To determine at which generation back an animal would have 262,144 ancestors, we need to solve for the number of generations (n) that gives us 2^n ancestors. We're looking for the generation where 2^n equals 262,144. Let's set up the equation:

2^n = 262,144

If we take the logarithm to the base of 2 on both sides of the equation, we get:

log2(2^n) = log2(262,144)

n = log2(262,144)

Since 262,144 is 2 raised to the 18th power, we get:

n = log2(2^18)

n = 18

An animal would have 262,144 ancestors 18 generations back.