Given data
*The amount of gold-198 is N = 100 g
*The gold-198 decays is n = 12.5 g
*The given time is T = 25.3 days
The expression for the radioactivity decay is given as
[tex]N=n(\frac{1}{2})^{\frac{T}{t}}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} 100=12.5(\frac{1}{2})^{\frac{25.3}{t}} \\ t=8.43\text{ days} \end{gathered}[/tex]