3 The variables \(y\) and \(x\) are related by an equation of the form
$$y = a \left( b ^ { x } \right)$$
where \(a\) and \(b\) are positive constants.
Let \(Y = \log _ { 10 } y\).
- Show that there is a linear relationship between \(Y\) and \(x\).
- The graph of \(Y\) against \(x\), shown below, passes through the points ( \(0,2.5\) ) and (5, 0.5).
\includegraphics[max width=\textwidth, alt={}, center]{7e7eaea5-22ca-4418-8ac6-351ce9ac09ea-06_433_506_904_776}
- Find the gradient of the line.
- Find the value of \(a\) and the value of \(b\), giving each answer to three significant figures. [4 marks]