- The value, \(\pounds V\), of a vintage car \(t\) years after it was first valued on 1 st January 2001, is modelled by the equation
$$V = A p ^ { t } \quad \text { where } A \text { and } p \text { are constants }$$
Given that the value of the car was \(\pounds 32000\) on 1st January 2005 and \(\pounds 50000\) on 1st January 2012
- find \(p\) to 4 decimal places,
- show that \(A\) is approximately 24800
- With reference to the model, interpret
- the value of the constant \(A\),
- the value of the constant \(p\).
Using the model,
- find the year during which the value of the car first exceeds \(\pounds 100000\)