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