We have an experiment which have the variables $x$ and $y$. $x$ and $y$ can be measured into pair $(x_i,y_i)$. Now I'm finding a way to interpolate it into a power function $y=a+bx^c$. Which $a,b,c$ are real number (and $a>0, b>0, c>0$). How to find that function? (among $a,b,c$; $a$ is the number I need the most). For example, we did the experiment many times and have $(x_1,y_1)=(1,3)$; $(x_2,y_2)=(3,5)$; $(x_3,y_3)=(5,8)$; $(x_4,y_4)=(10,11)$
If possible, how can we do that in Matlab (or similar programming software)?