Question

A laptop computer is purchased four 4400 dollars. Each year, it's value is 75% of it's value the year before. After how many years will the laptop computer be worth 900 dollars or less? Write the smallest possible whole number answer

Answer 1

We will determine the time it will take to be worth $900 or less as follows:

`\begin{gathered} 900=4400(0.75)^x\Rightarrow(9)/(44)=(0.75)^x \\ \\ \Rightarrow ln((9)/(44))=xln(0.75)\Rightarrow x=(ln(9/44))/(ln(0.75)) \\ \\ \Rightarrow x=5.516384956...\Rightarrow x\approx6 \end{gathered}`

So, it will be approximately 6 years until the laptop is worth $900 or less.