Answer
5200 years.
Work Step by Step
$N_{0}=16.1/min \cdot g\,C$
$N= 8.6/min \cdot g\,C$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{5730\,y}=1.2094\times10^{-4}/y$
$\ln(\frac{N_{0}}{N})=kt$
$\implies \ln(\frac{16.1}{8.6})=0.627=$$(1.2094\times10^{-4}/y)\times t$
$\implies t=\frac{0.627}{1.2094\times10^{-4}\,y^{-1}}=5200\,y$
