You as the engineer on a project employing a FEM analysis are responsible for refining the mesh. You decide to inspect the computational complexity of the solver employed by your software. You initially have a two dimensional mesh of $10$ x $10$ nodes with an analysis run time of $1\mathrm{.}2$ seconds. You refine the mesh by a factor of $3$ in each direction to obtain a mesh of $30$ x $30$ nodes with an analysis run time of $222\mathrm{.}1$ seconds. In order to predict the future run time of different mesh sizes you assume the following relation:

tcpu$$n$\backslash$beta

Assume the number of nodes forming part of the Dirichlet boundary conditions to be negligible in comparison with the total number of nodes in the mesh. Determine the constant $\backslash$beta

to three decimal places.