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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?

1 Answer

Dec 26, 2015

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

Explanation:

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

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

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

...

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

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