Question

A car is purchased for $33,000. Each year it loses 30% of its value. After how many years will the car be worth $4900 or less? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.

Answer 1

Given:

A car is purchased for $33,000.

Each year it loses 30% of its value

The value of the car (y) after (x) years will be as follows:

`y=33000(1-(30)/(100))^x`

We will find (x) when y = 4900

`\begin{gathered} 4900=33000(1-(30)/(100))^x \\ (4900)/(33000)=0.7^x \\ \\ ln((4900)/(33000))=x*ln(0.7) \\ \\ x=(ln((4900)/(33000)))/(ln(0.7))=5.347 \end{gathered}`

Rounding to the smallest possible whole number

So, the answer will be the number of years = 5