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?

(N/A) The rate constant of a chemical reaction generally increases with an increase in temperature. For many reactions,the rate constant is nearly doubled with a rise in temperature by $10^{\circ}C$.
The temperature effect on the rate constant is represented quantitatively by the Arrhenius equation:
$k = A e^{-E_a / RT}$
Where:
$k$ is the rate constant,
$A$ is the Arrhenius factor (or frequency factor),
$E_a$ is the activation energy for the reaction,
$R$ is the gas constant,
$T$ is the temperature in Kelvin.