Time taken is given by :
[tex]t=-\dfrac{1}{k}\dfrac{[A_t]}{[A_o]}[/tex] .......( 1 )
Also,
[tex]k = \dfrac{0.693}{t_{0.5}}\\\\\\k=\dfrac{0.693}{0.5}\\\\k=2\times 0.693\ year^{-1}[/tex]
Putting value of k in equation 1, we get :
[tex]t=\dfrac{1}{2\times 0.693}\times ln(\dfrac{2}{16})\\\\t=1.5\ years[/tex]
Therefore, time taken is 1.5 years.
Hence, this is the required solution.