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Carbon-14 has a half-life of approximately 5,730 years. This exponential decay can be modeled with the function N(t) = N0.

If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.

Carbon14 has a halflife of approximately 5730 years This exponential decay can be modeled with the function Nt N0 If an organism had 200 atoms of carbon14 at de class=

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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200\\ t=\textit{elapsed time}\dotfill &14325\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=200\left( \frac{1}{2} \right)^{\frac{14325}{5730}}\implies A=200\left( \frac{1}{2} \right)^{\frac{5}{2}}\implies A\approx 35.36[/tex]

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