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:

$y=33000(1-\frac{30}{100})^x$

We will find (x) when y = 4900

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

Rounding to the smallest possible whole number

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