1. How do I know whether to use an exponential model or a power function model?

In an examination, there will be clues in the question, e.g. You will be asked to draw a log-log graph which hints at a power function model.

In real life, by looking at the data you may be able to detect an exponential-type function. Otherwise, plot both types of graph (log-log and semi-log) and see which gives the best straight line.

2. Do ALL of the points need to fit EXACTLY into the straight lines produced when modelling?

The modelling is often only approximated by the mathematical function. Values from an experiment may differ from that predicted due to experimental error, mis-readings or a range of other factors.