Question #d0547

Question

Question #d0547

1 Answer

Impact of this question

1725 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-03T01:57:40

$21000 years$ $21000 "years"$

Explanation:

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

So now we want to solve

$\frac{1}{2^{x}} = 8 %$ $1/2^x = 8%$

Which is

$x = {log}_{2} (\frac{1}{8 %})$ $x = log_2(1/(8%))$

$\approx 3.64$ $~~ 3.64$

In terms of number of years, it would be

$x \cdot (5700 years) = 3.64 \cdot (5700 years)$ $x * (5700 "years") = 3.64 * (5700 "years")$

$\approx 21000 years$ $~~ 21000 "years"$

Science

Math

Humanities

... and beyond

Question #d0547

1 Answer

Explanation:

Related questions

Impact of this question