# 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

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

Keywords:Exponential Fit