In general, the values are empirically derived. K is a function of the physical properties of the drug delivery system, while the exponent, n, tells you something about the release mechanism, whether the diffusion is governed by Fick's law or not.

So you do some experiments, collect data as a function of time, fit the data with the Peppas model, and then, if the fit is adequate, you can draw some conclusions about the physical process going on.

If you want to obbtain the Peppas parametes(a,k,n),you can use Microsoft Solver to get them.

first,you do some tests,collect data as a function of time

second,you give a Initial value about a,k,n

third,caculate the Fitted values

fouth,use Microsoft Solver to get Peppas Paramets(a,k,n).

Ps:I give you a Peppas Model file you can use it.

Just a note on the methods of fitting to the Peppas equation.  Mt/M_inf=K*t^n is only applicable in the range of Mt/M_inf < 0.60.  This is an assumption in the empirical derivation of the equation.  The literature is riddled with misapplication of the equation as it is easy to implement but the interpretation usually gets muddled.  Find the original papers if you can as they will give you the best insight into how to apply the equations.

Edit1:  Below is a publication which outlines the semi-empirical derivation of the Peppas equation as well as demonstrates how to apply it.

Article Polyplex Formation Influences Release Mechanism of Mono- and...

You can use the origin software to find the variable, after tracing your curve, go to the analysis => fitting=> non-linear curve fit, define a new function (peppas function) with two parameters of K and n, then when you are curve fitting to the your results it will find the related values of K