Question

How long ago, to the nearest year, was the artifact made?

Answer 1

Let's use the following formula:

`A=A_0(0.5)^{(t)/(h)}`

where:

Ao= Initial amount

t = time

h = half-life

`\begin{gathered} A=0.2A_0 \\ so\colon \\ 0.2A_0=A_0(0.5)^{(t)/(5730)} \end{gathered}`

solve for t:

`\begin{gathered} 0.2=0.5^{(t)/(5730)} \\ \ln (0.2)=(t)/(5730)\ln (0.5) \\ t=5730\cdot(\ln (0.2))/(\ln (0.5)) \\ t\approx13305 \end{gathered}`