Given a specific set of coordinates, I'm trying to write an equation that will describe their curve.
By graphing the coordinates, I believe it should be a cubic equation. But there is only one root at $(0,0)$.
The coordinates are as follows: $(0,0)$, $(2.1258,15)$, $(4.5809,30)$, $(7.8878,45)$, $(13.6083,60)$, $(27.2268,75)$, $(57.1741,85)$, $(90,90)$, $(121.4014,95)$, $(152.3215,105)$, $(166.4417,120)$, $(177.8625,165)$, $(175.4013,150)$, $(180,180)$
I have been reading and watching video tutorials about cubic equations but they're all either given the equation or given multiple roots.
The closest equation I've been able to write (guess, really) is as follows, but it doesn't quite follow the curve. $$p(x)=0.0001(x-90)^3+90$$
I am not looking for you to tell me the equation, I want to learn how to write them. Any help is greatly appreciated.
Perhaps it would be relevant to mention that there are limits to the Y value, when $x<90$ then $y<90$, the opposite is also true. Not sure if this changes anything, though.