Answer
2770 years.
Work Step by Step
Decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{5730\,y}=1.21\times10^{-4}\,y^{-1}$
$\ln(\frac{A_{0}}{A})=kt$
$\implies \ln(\frac{0.260}{0.186})=0.3349=1.21\times10^{-4}\,y^{-1}(t)$
Then, $t=\frac{0.3349}{1.21\times10^{-4}\,y^{-1}}=2.77\times10^{3}\,y$
