Chapter 3.2, Problem 54PE

In 2006, the murder of Alexander Litvinenko a Russian dissident, was through to be by poisoning from the rare and highly radioactive element poloninum-210 $\left({}^{210}\text{Po}\right).$ The half-life of ${}^{210}\text{Po}$ is 138.4 yr. If 0.1 mg of ${}^{210}\text{Po}$ is present in a sample then $A\left(t\right)=0.1{\left(\frac{1}{2}\right)}^{t/138.4}$ gives the amount $A\left(t\right)\left(\text{in mg}\right)$ present after t years. Evaluate the function for the given values of t and interpret the meaning in context. Round to 3 decimal places if necessary.

$\begin{array}{l}\text{a}\text{. }A\left(138.4\right)\\ \text{b}\text{. }A\left(276.8\right)\\ \text{c}\text{. }A\left(500\right)\end{array}$