I'll use this thread instead of creating a new one. I'm working on creating emphiric functions given various datasets.
Linear functions and as shown above exponential functions are fine.
Now I'm working with functions that are similar to exponential functions, but using log.
I want a function of the form: [latex]f(x) = c * x^r[/latex]
The data set:
[latex](\log{x_0}, \log{y_0}), (\log{x_1}, \log{y_1}).[/latex]
There might obviously be more points. From these points, we try to draw out a straight line as possible on a graph. Then find the graphs slope(?) graphically with a ruler. ie
[latex]\frac{\Delta x}{\Delta y} = r[/latex]
Now we have:
[latex]c * x_0^r = y_0 \rightarrow c = \frac{y_0}{x_0^r}[/latex]
I've tried this out with various data, but my function is always very inaccurate. It's 100% for the point I use to find 'c', but for any other point the result might be as much as 50% off. I know it's an emphiric function, but I would expect I would be able to get it more accurate.
Is this normal?
