Answer
30.3 years
Work Step by Step
Percentage remaining=$\frac{N}{N_{0}}\times100\%=89.2\%$
$\implies \frac{N}{N_{0}}=\frac{89.2}{100}=0.892$
$t=5.00\,y$
Recall that $\ln(\frac{N}{N_{0}})=-kt$
$\implies \ln(0.892)=-0.11429=-k(5.00\,y)$
Or decay constant $k=\frac{0.11429}{5.00\,y}=0.022858\,y^{-1}$
Half-life can be determined from $k$ as below:
$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.022858\,y^{-1}}=30.3\,y$
