Chapter 4.2, Problem 54PE

In 2006, the murder of Alexander Litvinenko, a Russian dissident, was thought to be by poisoning from the rate and highly radioactive element polonium-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 $A\left(t\right)$

(in mg) 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.

a. $A\left(138.4\right)$

b. $A\left(276.8\right)$

c. $A\left(500\right)$