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: 2/4/2015

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