# Question d0547

Mar 3, 2016

$21000 \text{years}$

#### Explanation:

For each half-life, the amount of $\text{C} - 14$ would be halved. So after $x$ number of half-lives, where $x$ is a positive integer, the amount of $\text{C} - 14$ left would be $\frac{1}{2} ^ x$. 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%))#

$\approx 3.64$

In terms of number of years, it would be

$x \cdot \left(5700 \text{years") = 3.64 * (5700 "years}\right)$

$\approx 21000 \text{years}$