Answer
a. $V_{n}=0.8^{n}(160,000)$
b. during the 3rd year
Work Step by Step
a.
Let $V_{n}$ be the value of the bulldozer after n years.
".. depreciates by $ 20\%$" = "equals $ 80\%$ of ..."
$V_{n}=0.8V_{n-1}$
With $V_{0}=160,000$
$V_{1}=0.8V_{0}=0.8(160,000)$
$V_{2}=0.8V_{1}=0.8^{2}(160,000)$
$...$
$V_{n}=0.8^{n}(160,000)$
b.
$V_{1}=128,000$
$V_{2}=102,400$
$V_{3}=81,920$
The value falls below $\$ 100,000$
during the 3rd year
