I'm trying to find the intersect between a linear function and a power (fractal) function. I thought all this would require is a simple bit of algebra. I've since broken my and several friends' heads over it and we keep getting stuck.
linear function: 18886 -233.7*x
power function: 3052000*x^-1.972
Bit of background: They are functions that describe product size from a ball mill for grinding minerals.
So basically, what I'm trying to solve is:
18886-233.7*x = 3052000*x^-1.972
I've rewritten this as:
18886 = 3052000 / x^1.972 + 233.7*x
18886*x^1.972 = 3052000 + 233.7*x^2.972
18886*x^1.972 - 233.7*x^2.972 = 305200
80.183*x^1.972 -x^2.972 = 13059.481
And this is more or less where I get stuck. Hope it is correct to this point... Would be great if someone could help me out with this.
Cheers in advance!!!