Question

How long do you think it would take for the material to decay to 23% (without doing the actual calculation), make an explanation using the half-life being 12 years

Answer 1

The exponential decay can be expressed as;

`A(t)=A_0((1)/(2))^{^{(t)/(t_(half))}}`
`\begin{gathered} \Rightarrow0.23=((1)/(2))^{(t)/(12)} \\ \\ \Rightarrow\ln(0.23)=(t)/(12)\ln((1)/(2)) \\ \\ \Rightarrow t=(12*\ln(0.23))/(\ln((1)/(2)))=25 \end{gathered}`

Hence, it will take about 25 years. (By calculation)

By Inspection.

12 years is 50%

24 years is 25%

It will take about 24 years to decay to 23%