The initial rate for the elementary reaction $A+2B3C$ in a constant$-$volume batch reactor was measured as a function of temperature when the concentration of A was $1M$ and that of B was $2\mathrm{.}5M$ and reported in the table below.

$\backslash$table$[[-r_A(mo\frac{l}{L}\frac{?}{s}),0\mathrm{.}00212,0\mathrm{.}00717,0\mathrm{.}0225,0\mathrm{.}0657,0\mathrm{.}180,0\mathrm{.}466,1\mathrm{.}14,2\mathrm{.}67],[T(C),25,35,45,55,65,75,85,95]]$

a$.$ What is the activation energy?

b$.$ What is the frequency factor?

c$.$ Write the rate constant as a function of temperature using $T=300K$ as the base case.