- (i) The variables \(x\) and \(y\) are connected by the equation
$$y = \frac { 10 ^ { 6 } } { x ^ { 3 } } \quad x > 0$$
Sketch the graph of \(\log _ { 10 } y\) against \(\log _ { 10 } x\)
Show on your sketch the coordinates of the points of intersection of the graph with the axes.
(ii)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a695b86-1660-4c06-ac96-4cdb07af9a2e-08_888_885_744_552}
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\caption{Figure 2}
\end{figure}
Figure 2 shows the linear relationship between \(\log _ { 3 } N\) and \(t\).
Show that \(N = a b ^ { t }\) where \(a\) and \(b\) are constants to be found.