I am struggling to find parameters $A$, $B$, $k_{1}$ and $k_{2} $ by fitting the following data points (50, 4.220455544), (100, 4.153915042), (150, 4.061640364) and (200, 3.750447771) to the function $f(t)=Ae^{-k_{1}t}-Be^{-k_{2}t}$.
I started by creating the following equations:
$f(50)=Ae^{-50k_{1}}-Be^{-50k_{2}}=4.220455544$
$f(100)=Ae^{-100k_{1}}-Be^{-100k_{2}}=4.153915042$
$f(150)=Ae^{-150k_{1}}-Be^{-150k_{2}}=4.061640364$
$f(200)=Ae^{-200k_{1}}-Be^{-200k_{2}}=3.750447771$
Any guidance on how to manually manipulate these equations to solve for parameters $A$, $B$, $k_{1}$ and $k_{2}$ (without use of any program including least squares fitting) will be appreciated.