Question

A car is purchased for 15,000. Each year it loses 30% of it's value. After how many years will the car be worth 4600 or less. Write the smallest possible whole number answer

Answer 1

We will have the following:

$\begin{gathered} 4600=15000(0.7)^x\Rightarrow\frac{23}{75}=(0.7)^x \\ \\ \Rightarrow ln(\frac{23}{75})=xln(0.7)\Rightarrow x=\frac{ln(23/75)}{ln(0.7)} \\ \\ \Rightarrow x=3.313924675...\Rightarrow x\approx3 \end{gathered}$

So, the after approximately 3 years the car will be worth $4600 or less.