Given:
Half-life = 1620 years
Original mass, m₀ = 220 g
The decay equation is of the form
[tex]m(t) = m_{0} e^{-kt}[/tex]
where
t = time, years
k = constant
At half-life, m = 0.5m₀ and t = 1620. Therefore
[tex]e^{-1620k} = 0.5 \\\\ -1620k = ln(0.5) \\\\ k = - \frac{ln(0.5)}{1620} =4.2787 \times 10^{-4}[/tex]
When t = 10 half-lives = 16200 years, obtain
[tex]m = (220 \, g) e^{-4.2787 \times 10^{-4}*16200}=0.2148 \, g[/tex]
Answer: 0.215 g (nearest thousandth)
