# Fit the Mitcherlich law in SAS

The data below represent the fraction of active chlorine in a chemical product as a function of time after manufacturing

Consider the model $$y=\theta_1 - \theta_2 e^{-\theta_3 x} + \varepsilon$$, called the Mitcherlich model. Fit the Mitcherlich law to these data and discuss how you obtained the starting values.

Can anybody help me figure out how to do this? I am using SAS and for now this is what i wrote

proc import datafile='/folders/myfolders/xlsx datasets/chlorine.xlsx'
dbms=xlsx
out=chlorine
replace;
getnames=yes;

*scatter plot;
proc sgscatter data= chlorine;
plot y*x / reg;
run;

*Fit the Mitcherlich law;
data chlorine;
set chlorine;
y2= log(0.4-y);
run;

proc reg data=chlorine;
model y2=x;
run;
quit;

proc nlin data=chlorine method=Marquardt;
parameters alpha=0.4 kappa=-0.06601 x0=45;
Mitcherlich = alpha*(1-exp(-kappa*(x-x0)));
model y = Mitcherlich;
run;