13.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{725966d1-d29d-4c9d-b850-c67d55cdd6e8-19_694_1246_344_534}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The value of a sculpture, \(\pounds V\), is modelled by the equation \(V = A p ^ { t }\), where \(A\) and \(p\) are constants and \(t\) is the number of years since the value of the painting was first recorded on \(1 ^ { \text {st } }\) January 1960.
The line \(l\) shown in Figure 4 illustrates the linear relationship between \(t\) and \(\log _ { 10 } V\) for \(t \geq 0\).
The line \(l\) passes through the point \(\left( 0 , \log _ { 10 } 20 \right)\) and \(\left( 50 , \log _ { 10 } 2000 \right)\).
a. Write down the equation of the line \(l\).
b. Using your answer to part a or otherwise, find the values of \(A\) and \(p\).
c. With reference to the model, interpret the values of the constant \(A\) and \(p\).
d. Use your model, to predict the value of the sculpture, on \(1 { } ^ { \text {st } }\) January 2020, giving your answer to the nearest pounds.