Direct and Inverse Proportion

A simplified model states that a car’s value \(V\) dollars is inversely proportional to its age \(a\) years, for \(a\ge1\). At age \(3\) years, its value is \(\$24,000\).

1. Find the equation connecting \(V\) and \(a\).

2. Find the predicted value at age \(8\) years.

3. Find the age at which the predicted value is \(\$12,000\).

4. Explain why this equation cannot assign a value at \(a=0\).