6 [Figure 1 and Figure 2, printed on the insert, are provided for use in this question.]
The variables \(x\) and \(y\) are known to be related by an equation of the form
$$y = k x ^ { n }$$
where \(k\) and \(n\) are constants.
Experimental evidence has provided the following approximate values:
| \(x\) | 4 | 17 | 150 | 300 |
| \(y\) | 1.8 | 5.0 | 30 | 50 |
- Complete the table in Figure 1, showing values of \(X\) and \(Y\), where
$$X = \log _ { 10 } x \quad \text { and } \quad Y = \log _ { 10 } y$$
Give each value to two decimal places.
- Show that if \(y = k x ^ { n }\), then \(X\) and \(Y\) must satisfy an equation of the form
$$Y = a X + b$$
- Draw on Figure 2 a linear graph relating \(X\) and \(Y\).
- Find an estimate for the value of \(n\).