Question

The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milligrams of 14C. How many milligrams of 14C should be in the bone fragment 10,000 years later? Round to the nearest tenth.

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 &6\\ t=years\dotfill &10000\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A = 6\left( (1)/(2) \right)^{(10000)/(5730)}\implies A = 6\left( (1)/(2) \right)^{(1000)/(573)}\implies A \approx 1.8`