Question

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.

Answer 1

`\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(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( (1)/(2) \right)^{(14325)/(5730)}\implies A=200\left( (1)/(2) \right)^{(5)/(2)}\implies A\approx 35.36`