Using the decay formula:
[tex]N=N_o(\frac{1}{2})^{\frac{T}{T_{1/2}}}[/tex]Where:
[tex]N=1891-832=1059[/tex]So:
[tex]\begin{gathered} 1059=1891(\frac{1}{2})^{\frac{T}{14.19}} \\ \frac{1059}{1891}=(\frac{1}{2})^{\frac{T}{14.19}} \\ 0.56=(\frac{1}{2})^{\frac{T}{14.19}} \\ \end{gathered}[/tex]Solve for T:
[tex]\begin{gathered} log(0.56)=\frac{T}{14.19}log(\frac{1}{2}) \\ T=14.19(\frac{log(0.56)}{log(\frac{1}{2})}) \\ T\approx11.87s \end{gathered}[/tex]Answer:
11.87 seconds
