Answer
a) $V_n=160000(0.8)^{n-1}$.
b) $n=4$.
Work Step by Step
a) If the original amount was $160000$ and it decreases by $20\%$ each year, then $V_n=160000(0.8)^{n-1}$.
b) Our inequality, according to the exercise is:
$100000\geq160000(0.8)^{n-1}\\0.625\geq(0.8)^{n-1}$.
If $n=3$, then $0.8^{n-1}=0.64\gt0.625$, but if $n=4$, then $0.8^{n-1}=0.512\leq0.625$, so it will be under $100000$ in $n=4$.
