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# The half-life of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 7 half lives?

Dec 26, 2015

(frac{1}{2})^7 = 1/128 ~~ 0.781%

#### Explanation:

After 1 half-life, $\frac{1}{2}$ of the C-14 would remain.

After 2 half-life, $\frac{1}{2}$ of the $\frac{1}{2}$ of the C-14 = $\frac{1}{4}$ of the C-14 would remain.

After 3 half-life, $\frac{1}{2}$ of the $\frac{1}{4}$ of the C-14 = $\frac{1}{8}$ of the C-14 would remain.

...

After $n$ half-lives, $\frac{1}{{2}^{n}}$ of the C-14 would remain.