Power law for orbital periods

For objects orbiting the same star, the period \(T\) years and the mean distance \(r\) (in astronomical units) are believed to satisfy \(T=cr^n\), where \(c\) and \(n\) are constants. Two objects have \((r,T)=(1,1)\) and \((4,8)\).

1. Explain why plotting \(\lg T\) against \(\lg r\) is better than plotting \(T\) against \(r\) when testing this law.[2]
2. Find \(c\) and the exact value of \(n\), and predict \(T\) for an object with \(r=9\).[3]
3. An object is reported with \(r=2\) and \(T=2.5\). Decide, with a calculation, whether this report fits the model.[2]