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In class on Friday, Dr. Lavelle showed us the Arrhenius equation, which is K=Ae^Ea/RT. This is another way of expressing the constant K and finding other components of the equation quantitatively. That is the equation used in this problem to find K.
You're correct that rate constant and rate are not the same thing; however, since this question asks for the factor by which the rate increases, and everything else stays the same, the factor between change in k and rate will be identical.
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