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\end{equation}  Experimentalists deduce rate laws from data corresponding to the integrated rate law. For the $i^{th}$-order reaction the traditional integrated rate law, with $k_i(t)\to\omega$ is  \begin{equation}  \frac{1}{[C_A(t)]^{i-1}} \frac{1}{C_A(t)^{i-1}}  = \frac{1}{[C_A(0)]^{i-1}}+(i-1)\omega \frac{1}{C_A(0)^{i-1}}+(i-1)\omega  t. \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) S_i(t)  = \frac{C_A(t)}{C_A(0)} \frac{C_{A^i}(t)}{C_{A^i}(0)}  = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_A(0)^{i-1}}}, tC_{A^i}(0)^{i-1}}},  \end{equation}  which come from the integrated rate law.