The measurement of radioactive decay can be useful tool in things such as Carbon-dating. For a carbon sample with mass 500kg and a half life of 5,730 years, calculate the remaining mass after 20,000years.

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cooper2017 cooper2017

18-01-2019
Mathematics

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The measurement of radioactive decay can be useful tool in things such as Carbon-dating. For a carbon sample with mass 500kg and a half life of 5,730 years, calculate the remaining mass after 20,000years.

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jdoe0001 jdoe0001 · Answer 1 · 2019-01-19T00:06:45+01:00

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &500\\ t=\textit{elapsed time}\dotfill &20000\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=500\left( \frac{1}{2} \right)^{\frac{20000}{5730}}\implies A\approx 0.00000001555302367~Kgs[/tex]