3.116 FAQ-676 We are trying to use a single exponential decay equation to determine the half-life of a compound, but your equation is slightly different than the standard form. How do we calculate the half-life?

Last Update: 2/3/2015

Typically, the standard form of the single exponential decay function is

\[ A(t) = A_0e^{-kt} \]

where \(A_0\) is the initial population, \(k\) is the decay constant, and \(t\) is time. In this case the formula for \(t\) is \(\frac {\ln(2)} {k}\).

In Origin's case, one of its single exponential decay equations (ExpDecay1) is described as:

\[y = y_0 + Ae^{\frac {-(x-x0)} {t}}\]

Suppose \(y_0 = 0\). The equation then becomes \(y = Ae^{\frac {-(x-x0)} {t}}\). If the equations are then set equal to each other and solved for \(k\) one finds that \(k=\frac {-(x-x_0)} {t^2}\). Since this is the case, the equation for a half-life becomes

\[t(\frac {1}{2}) = x_0 + t\ln(2)\]

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Keywords:Exponential Fit