10 A function \(y = \mathrm { f } ( x )\) may be modelled by the equation \(y = a x ^ { b }\).
- Show why, if this is so, then plotting \(\log y\) against \(\log x\) will produce a straight line graph. Explain how \(a\) and \(b\) may be determined experimentally from the graph.
- Values of \(x\) and \(y\) are given below. By plotting a graph of logy against log \(x\), show that the model above is appropriate for this set of data and find values of \(a\) and \(b\) given that \(a\) is an integer and \(b\) can be written as a fraction with a denominator less than 10 .
| \(x\) | 2 | 3 | 4 | 5 | 6 |
| \(y\) | 4.6 | 5.0 | 5.3 | 5.5 | 5.7 |
- Use your formula from part (ii) to estimate the value of \(y\) when \(x = 2.8\).