Question

Carbón 11 had a half-life if about 20minutes.if we start with 200 grams ,how much will be lift after 3 hours

Answer 1

Now, there are 60 minutes in 1 hour, thus 20 minutes is just 20/60 or 1/3 of an hour.

$\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &200\\ t=\textit{elapsed time}\to &3\\ h=\textit{half-life}\to &\frac{1}{3} \end{cases} \\\\\\ A=200\left( \frac{1}{2} \right)^{\frac{~3~}{\frac{1}{3}}}\implies A=200\left( \frac{1}{2} \right)^{\frac{3}{1}\cdot \frac{3}{1}}\implies A=200\left( \frac{1}{2} \right)^9 \\\\\\ A=0.390625$