4 The variables \(x\) and \(Y\), where \(Y = \log _ { 10 } y\), are related by the equation
$$Y = m x + c$$
where \(m\) and \(c\) are constants.
- Given that \(y = a b ^ { x }\), express \(a\) in terms of \(c\), and \(b\) in terms of \(m\).
- It is given that \(y = 12\) when \(x = 1\) and that \(y = 27\) when \(x = 5\).
On the diagram below, draw a linear graph relating \(x\) and \(Y\).
- Use your graph to estimate, to two significant figures:
- the value of \(y\) when \(x = 3\);
- the value of \(a\).
\includegraphics[max width=\textwidth, alt={}, center]{7441c4e6-5448-483b-b100-f8076e7e6cd8-3_976_1173_1110_484}