1. The value of a car is modelled by the formula

$$V = 16000 \mathrm { e } ^ { - k t } + A , \quad t \geqslant 0 , t \in \mathbb { R }$$ where \(V\) is the value of the car in pounds, \(t\) is the age of the car in years, and \(k\) and \(A\) are positive constants. Given that the value of the car is \(\pounds 17500\) when new and \(\pounds 13500\) two years later,

1. find the value of \(A\),
2. show that \(k = \ln \left( \frac { 2 } { \sqrt { 3 } } \right)\)
3. Find the age of the car, in years, when the value of the car is \(\pounds 6000\) Give your answer to 2 decimal places.