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\end{equation}  From the integrated rate law, we get the survival function  \begin{equation}  S(t)=\frac{C_A(t)}{C_A(0)}=\sqrt[n-1]{\frac{1}{1+(n-1)\omega t[A_0]^{n-1}}} tC_A(0)^{n-1}}}  \end{equation}  From the survival function, the time dependent rate coefficient is  \begin{equation}