eli5: Why is x^0=1?

Question

I’m confused, shouldn’t it be 0?

In: Mathematics

Answer 1

I’ll illustrate it with an example:

Suppose we have a population of some species that reproduces asexually. Let’s say that each individual produces an offspring every hour.

1 hour from now, we will have twice the current population.

2 hours from now, we will have four (or 2^(2)) times the current population.

3 hours from now, we will have eight (or 2^(3)) times the current population.

Now, if I asked you what will the population size be in 0 hours, by what factor would you multiply?