11 A student records the time a pendulum takes to swing for different lengths of pendulum. The student decides to plot a graph of \(\log _ { 10 } T\) against \(\log _ { 10 } l\) where \(T\) is the time in seconds that the pendulum takes to return to its start position and \(l\) is the length in metres of the pendulum. They use a model for \(\log _ { 10 } T\) in terms of \(\log _ { 10 } l\) of the form \(\log _ { 10 } T = \log _ { 10 } \mathrm { k } + \mathrm { n } \log _ { 10 } \mathrm { l }\). The student records the following data points.

1. Determine the values of \(k\) and \(n\) that best model the data. Give your values correct to 2 significant figures.
2. Using these values of \(k\) and \(n\), write the student's model as an equation expressing \(T\) in terms of \(l\).