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This comes from the integrated rate law for a first order reaction. The equation is ln[A]=-kt+ln[A]o. If we take everything and raise e to that power, we get e^ln[A]=e^-kt+e^ln[A]o. the terms on the right side can be added (since they have the same base) to become e^(-kt + ln[A]o). e^ln[A] becomes just [A], and e^ln[A]o becomes just [A]o, so the equation is changed into [A]=[A]o(e^-kt). Hope this helps!
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