I'm trying to fit values from this model $$y(x)=ae^{−bx}+c$$
where a, b and c are 3 different parameters that I want to find with least squares. So using least squares I want to find the value of a, b and c using this formula
$$ \mathrm{argmin}\sum_i \left( ae^{−bx_i}+c - y_i \right)^2. $$
This leads me to 3 non linear equations after partial derivation of the previous one with respect a, b and c. Surely there are already the general formula for this case but I cannot find them. Can anybody help me?