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\begin{equation}  \frac{dC_i(t)}{dt} = k_i(t)\left[C_i(t)\right]^i.  \end{equation}  Experimental data is typically a concentration profile corresponding to the integratedform of the  rate law. Normalizing If  the concentration profile, by comparing dividing  the concentration at a time $t$ to the initial concentration, leads to it is called  the survival function \begin{equation}  S_i(t) = \frac{C_i(t)}{C_i(0)},  \end{equation}  which we will use as the input to our theory. Namely, we define the effective rate coefficient, $k_i(t)$, through an appropriate time derivative of the survival function that depends on the order $i$ of reaction \begin{equation}  k_i(t) \equiv  \begin{cases}