Answer
$2.34\times10^{9}\,y$
Work Step by Step
Rate constant $k= \frac{0.693}{t_{1/2}}=\frac{0.693}{703\times10^{6}\,y}$
$=9.85775\times10^{-10}\,y^{-1}$
We can obtain the time taken using integrated rate law which is
$\ln \frac{N_{t}}{N_{0}}=-kt$
$\ln \frac{10}{100}=-9.85775\times10^{-10}\,y^{-1}\times t$
$\implies -2.302585=-9.85775\times10^{-10}\,y^{-1}\times t$
$\implies t=\frac{-2.302585}{-9.85775\times10^{-10}\,y^{-1}}$
$=2.34\times10^{9}\,y$
