Question

Question #d0547

Answer 1

`21000 "years"`

Explanation:

For each half-life, the amount of `"C"-14` would be halved. So after `x` number of half-lives, where `x` is a positive integer, the amount of `"C"-14` left would be `1/2^x`. Turns out that this also works for `x` not being an integer (but `x` still has to be positive).

So now we want to solve

`1/2^x = 8%`

Which is

`x = log_2(1/(8%))`

`~~ 3.64`

In terms of number of years, it would be

`x * (5700 "years") = 3.64 * (5700 "years")`

`~~ 21000 "years"`