Non linear regression models are difficult to adjust, specially if they have more than one independent variable.
There some software that allows to do it. But in most cases adjustment are not as good as you can expect.
One of the basics about curve fitting is residuals.
Residuals (yreal - ypredicted)^2 allows to know how good is the fitting made. For example R is based on residuals.
One of the most used techniques to adjust multivariable models is to apply optimization to residuals.
When residuals are minimize difference between real and predicted trends are minimal. This way can be obtain the constants from the non linear model that provides the best possible fit.