8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{03548211-79cb-4629-b6ca-aa9dfcc77a33-13_743_1198_219_372}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The value of Lin's car is modelled by the formula
$$V = 18000 \mathrm { e } ^ { - 0.2 t } + 4000 \mathrm { e } ^ { - 0.1 t } + 1000 , \quad t \geqslant 0$$
where the value of the car is \(V\) pounds when the age of the car is \(t\) years.
A sketch of \(t\) against \(V\) is shown in Figure 1.
- State the range of \(V\).
According to this model,
- find the rate at which the value of the car is decreasing when \(t = 10\)
Give your answer in pounds per year.
- Calculate the exact value of \(t\) when \(V = 15000\)