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\begin{equation}  \frac{-dA}{dt}=\omega[A]  \end{equation}  The mechanism of each irreversible decay reaction may be different. For example, the irreversible decay of A into B may follow second order kinetics, where the rate law is  \begin{equation}  \frac{-dA}{dt}=\omega[A]^2  \end{equation}  The time dependent rate coefficient, k(t), is determined by integrating the rate law of the reaction and forming a survival function from the integrated rate law. From the survival function, the time dependent rate coefficient is determined by taking various time derivatives of the survival function, depending on the total order of reaction. For first order irreversible decay reactions, the time dependent rate coefficient is the negative time derivative of the natural log of the survival function[insert citation]  \begin{equation}  \frac{-dlnS(t)}{dt}=k(t)