It is thought that the variables [tex]$s$[/tex] and [tex]$t$[/tex] satisfy a relation of the form [tex]$\left(\frac{s}{t}\right)^p = q e^{-t}$[/tex] where the constants [tex]$p$[/tex] and [tex]$q$[/tex] are positive integers.

By drawing a linear graph, find the values of [tex]$p$[/tex] and [tex]$q$[/tex].

\begin{tabular}{|c|c|c|c|c|c|}
\hline
[tex]$t$[/tex] & 0.2 & 0.4 & 0.6 & 0.8 & 1.0 \\
\hline
[tex]$s$[/tex] & 1.09 & 1.96 & 2.67 & 3.22 & 3.64 \\
\hline
\end{tabular}