Question

You have 6,368 grams of a radioactive kind of cobalt. If its half-life is 271 days, how much

will be left after 542 days?

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 &6368\\ t=\textit{elapsed time}\dotfill &542\\ h=\textit{half-life}\dotfill &271 \end{cases} \\\\\\ A=6368\left( (1)/(2) \right)^{(542)/(271)}\implies A=6368\left( (1)/(2) \right)^2\implies A=1592`