I have this function which I wish to plot: $y=b(a-x)^{8/25}$
I have the values for $x,y$ as part of a data set, with thousands of values. This is in a file. What i have found is that $x$ is between 0 and 5 and $y$ is between 0 and 1.
I tried rearranging the equation to solve for $a$ and $b$, but I am still not sure what to do with that information
My main problems are that I dont know how to plot $a,b$ in a single graph that represents all values in the $x,y$ range. A secondary problem might be that I don't know how to write the equation properly, given what I am trying to do. And a tertiary concern is that I am also unsure how to get this into a graphing program. Insights are welcome.
I suspect that what you're really trying to do is find $a$ and $b$ that best fit the equation $y = b (a-x)^{8/25}$, and further that "best fit" is in the least squares sense, i.e. you want to minimize $$ \sum_i (y_i - b(a-x_i)^{8/25})^2$$ where $(x_i, y_i)$ are your data points. This is a non-linear least squares problem, so it is not easy, but methods are available on various software systems (Matlab, Maple, Sage, etc.).