An Arrhenius calculator

You will write three functions for the Arrhenius equation. One finds the rate constant. One finds the activation energy from two readings. One fits a straight line to a table of readings.

The idea. $k = Ae^{-E_a/RT}$. For two temperatures, $E_a = \dfrac{R\ln(k_2/k_1)}{1/T_1 - 1/T_2}$. A straight line of $\ln k$ against $1/T$ has slope $-E_a/R$.

Your tasks.

1. Complete rate_constant(pre_factor, ea, T) so that it returns $k$. The activation energy ea is in kJ/mol.
2. Complete activation_energy(k1, t1, k2, t2) so that it returns $E_a$ in kJ/mol.
3. Complete fit(temperatures, rates) so that it returns the activation energy in kJ/mol from the slope of the line.