Inverse Proportion: Car Value and Age

The value of a car, \(\$C\), is inversely proportional to its age, \(Y\) years. The value of a car after 3 years is \(\$54\,000\).

1. Write down an equation connecting \(C\) and \(Y\).
2. Find the value of the car after 5 years.
3. In how many years should the owner sell the car before the car is worth less than \(\$20\,000\).

For part (c), distinguish the age of the car from additional years from now. The model gives an age limit of \(8.1\) years; a current age is needed to calculate an additional waiting time.