Answer :
It will take 42.9 days
Further explanation
General formulas used in decay:
[tex]\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{T/t\frac{1}{2} }}}[/tex]
T = duration of decay
t 1/2 = half-life
N₀ = the number of initial radioactive atoms
Nt = the number of radioactive atoms left after decaying during T time
t1/2=14.3 days
Nt/No=1/8
[tex]\tt Nt=No(\dfrac{1}{2})^{T/t1/2}\\\\\dfrac{Nt}{No}=\dfrac{1}{2}^{T/t1/2}\\\\\dfrac{1}{8}=\dfrac{1}{2}^{T/t1/2}\\\\(\dfrac{1}{2})^3=\dfrac{1}{2}^{T/t1/2}\\\\3=T/14.3\rightarrow T=42.9~days[/tex]