Answer
6700 yr
Work Step by Step
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, $N_{0}$ is the original activity and $N$ is the present activity.
$\implies \ln(\frac{9200}{4100})=0.8082=(1.21\times10^{-4}\,y^{-1})\times t$
Or $t=\frac{0.8082}{1.21\times10^{-4}y^{-1}}=6700\,yr$
