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\end{equation}  Survival functions are the input to our theory. They are a measure of the concentration of species at a time $t$ compared to the initial concentration  \begin{equation}  S(t) = \frac{C_A(t)}{C_A(0)}, \frac{C_A(t)}{C_A(0)} = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_A(0)^{i-1}}},  \end{equation}  which come from the integrated rate law.The survival function for this class of reactions is  \begin{equation}  S(t) = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_A(0)^{i-1}}}  \end{equation}