Answer
1100 years.
Work Step by Step
Original activity of radionuclide
$N_{0}=16.0/min\cdot g\,C$
Present activity $N=14.0/min\cdot g\,C$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{5730\,y}=1.21\times10^{-4}\,y^{-1}$
$\ln(\frac{N_{0}}{N})=kt$ where $t$ is the age.
$\implies \ln(\frac{16.0}{14.0})=0.13353=1.21\times10^{-4}\,y^{-1}\times t$
Or $t= \frac{0.13353}{1.21\times10^{-4}\,y^{-1}}=1100\,years$
