Activation energy of any reaction depends on

What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?

Subtract $(i)$ $\ln \, k_1 = - \frac{E_a}{R T_1} + \ln A$ and $(ii)$ $\ln \, k_2 = - \frac{E_a}{R T_2} + \ln A$ and write the resulting equation.

The velocity constant of a reaction at $290 \ K$ was found to be $3.2 \times 10^{-3}$. At $310 \ K$,it will be about:

For a certain reaction,consider the plot of $\ln k$ versus $1/T$ given in the figure. If the rate constant of this reaction at $400 \ K$ is $10^{-5} \ s^{-1}$,then the rate constant at $500 \ K$ is:

For the reaction $CH_{3}CH_{2}CH_{2}I + OH^{-} \rightarrow CH_{3}CH_{2}CH_{2}OH + I^{-}$,the rate constant is $1.84 \ (mol \ L^{-1})^{-1} \ min^{-1}$ at $27^{\circ}C$ $(300 \ K)$ and $38.84 \ (mol \ L^{-1})^{-1} \ min^{-1}$ at $327 \ K$. Calculate the activation energy $(E_{a})$ in $cal \ mol^{-1}$.