N2009 P2 Q6

The table gives the world record time, in seconds above 3 minutes 30 seconds, for running 1 mile as at 1st January in various years.

1. Draw a scatter diagram to illustrate the data.[2]
2. Comment on whether a linear model would be appropriate, referring both to the scatter diagram and the context of the question.[2]
3. Explain why in this context a quadratic model would probably not be appropriate for long-term predictions.[1]
4. Fit a model of the form \(\ln t=a+bx\) to the data, and use it to predict the world record time as at 1st January 2010. Comment on the reliability of your prediction.[3]