Asymptotic Behavior of the Model Equations

Quite often the asymptotic behavior of the model can aid us in determining sufficiently good initial guesses. For example, let us consider the Michaelis-Menten kinetics for enzyme catalyzed reactions, 

When Xj tends to zero, the model equation reduces to 

Let us also consider the following exponential decay model, often encountered in analyzing environmental samples, 

In some cases we may not be able to obtain estimates of all the parameters by examining the asymptotic behavior of the model. However, it can still be used to obtain estimates of some of the parameters or even establish an approximate relationship between some of the parameters as functions of the rest. 

---