Analysis of exponential time constants

A graphical method for determining the decay time constant was mentioned some time ago (Mangelsdorf, 1959  

Livesey, 1979). Mangelsdorf pointed out that a function linear in exp(-t/Tj) has a linear relationship with any other function linear in exp(-t/T ). In particular, eq. (1) and 

The main drawback of this method is that if At/T 1 the slope exp(-At/Tj) is not too different from 1 and it is quite insensitive to At/T. On the other hand, we cannot let At/Tj 1 because 95% of the signal will have recovered in 3T so not very many values of Y(t+At) can be taken. 

An easy way of overcoming this difficulty has been known for half a century or more. In fact, Mangelsdorf s method is a special case of a method by Guggenheim (1926) 

we can plot Y/-Yj vs. t on semi-log paper to get T from the slope. What this amounts to is to take data points Y. and compare them with points Y/ taken fit (equal to one or two time constants) later instead of with Y( ) taken five or more time-constants later. 

---