- The value of Bob's car can be calculated from the formula
$$V = 17000 \mathrm { e } ^ { - 0.25 t } + 2000 \mathrm { e } ^ { - 0.5 t } + 500$$
where \(V\) is the value of the car in pounds \(( \pounds )\) and \(t\) is the age in years.
- Find the value of the car when \(t = 0\)
- Calculate the exact value of \(t\) when \(V = 9500\)
- Find the rate at which the value of the car is decreasing at the instant when \(t = 8\). Give your answer in pounds per year to the nearest pound.