System of eqs

Hi,

given the following system,

$ \begin{aligned} v(t_1) &=& b_1 + b_2e^{-t_1/b_3} + b_4e^{-t_1/b_4} \\ v(t_2) &=& b_1 + b_2e^{-t_2/b_3} + b_4e^{-t_2/b_4} \\ v(t_3) &=& b_1 + b_2e^{-t_3/b_3} + b_4e^{-t_3/b_4} \\ v(t_4) &=& b_1 + b_2e^{-t_4/b_3} + b_4e^{-t_4/b_4} \\ \end{aligned} $

where times $t_1,\dots,t_4$ and measurements $v(t_1),\cdots,v(t_4)$ are known, find constants $b_1,\dots,b_4$ .

I have not had much about nonlinear systems, but perhaps Newton's would work well enough for something like this. What do you guys think?