4 The variables \(x\) and \(y\) are known to be related by an equation of the form
$$y = a b ^ { x }$$
where \(a\) and \(b\) are constants.
- Given that \(Y = \log _ { 10 } y\), show that \(x\) and \(Y\) must satisfy an equation of the form
$$Y = m x + c$$
- The diagram shows the linear graph which has equation \(Y = m x + c\).
\includegraphics[max width=\textwidth, alt={}, center]{932d4c7e-6514-4543-b1d1-753fca5a08fd-5_744_720_833_699}
Use this graph to calculate:
- an approximate value of \(y\) when \(x = 2.3\), giving your answer to one decimal place;
- an approximate value of \(x\) when \(y = 80\), giving your answer to one decimal place.
(You are not required to find the values of \(m\) and \(c\).)