11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0839eb5f-2850-4d77-baf7-a6557d71076e-28_590_739_219_671}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The value, \(V\) pounds, of a mobile phone, \(t\) months after it was bought, is modelled by
$$V = a b ^ { t }$$
where \(a\) and \(b\) are constants.
Figure 2 shows the linear relationship between \(\log _ { 10 } V\) and \(t\).
The line passes through the points \(( 0,3 )\) and \(( 10,2.79 )\) as shown.
Using these points,
- find the initial value of the phone,
- find a complete equation for \(V\) in terms of \(t\), giving the exact value of \(a\) and giving the value of \(b\) to 3 significant figures.
Exactly 2 years after it was bought, the value of the phone was \(\pounds 320\)
- Use this information to evaluate the reliability of the model.