Question

The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?

Answer 1

50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.

Answer 2

`\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( (1)/(2) \right)^{(20)/(20)}\implies A=100\left( (1)/(2) \right)^1\implies A=50`