Solution
The exponential decay can be expressed as;
[tex]A(t)=A_0(\frac{1}{2})^{^{\frac{t}{t_{half}}}}[/tex][tex]\begin{gathered} \Rightarrow0.23=(\frac{1}{2})^{\frac{t}{12}} \\ \\ \Rightarrow\ln(0.23)=\frac{t}{12}\ln(\frac{1}{2}) \\ \\ \Rightarrow t=\frac{12\times\ln(0.23)}{\ln(\frac{1}{2})}=25 \end{gathered}[/tex]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%
