$\overline{)\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{A}\mathbf{\xb7}{\mathbf{e}}^{\mathbf{-}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{RT}}}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{A}\mathbf{\xb7}{\mathbf{e}}^{\mathbf{-}\frac{\mathbf{E}}{\mathbf{8}\mathbf{.}\mathbf{314}\mathbf{\times}\mathbf{310}\mathbf{.}\mathbf{15}}}\phantom{\rule{0ex}{0ex}}{\mathbf{k}}_{\mathbf{cat}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{A}\mathbf{\xb7}{\mathbf{e}}^{\mathbf{-}\frac{{\mathbf{E}}_{\mathbf{cat}}}{\mathbf{8}\mathbf{.}\mathbf{314}\mathbf{\times}\mathbf{310}\mathbf{.}\mathbf{15}}}$

Suppose that a certain biologically important reaction is quite slow at physiological temperature (37 ^{o}C) in the absence of a catalyst.

Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction in order to achieve a 4×10^{5}-fold increase in the reaction rate?

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