9.
Two models are proposed for the value of a car.
- The first model suggests that the value of the car, \(V\) pounds, is given by \(V = 18000 - 6000 \sqrt { t }\), where \(t\) is the time in years after the car was first purchased.
- State the value of the car when it was first purchased.
- (ii) Find \(V\) and \(\frac { \mathrm { d } V } { \mathrm {~d} t }\) when \(t = 4\)
- (iii) Interpret your answers to (a)(ii) in the context of the model.
- The second model that is proposed suggests that the value of the car, \(V\) pounds, is given by \(V = a b ^ { - t }\), where \(t\) is the time in years after the car was first purchased.
When \(t = 0\), both models give the same value for \(V\).
When \(t = 4\), both models give the same value for \(V\).
Find the value of \(a\) and the value of \(b\).
[0pt]
[3 marks] - Explain, with a reason, which model is likely to be the better model over time.