So I'm working on a small project that will use a calculation in excel, I'm nearly there and the only piece missing is being able to accurately estimate a data point from the following set of data points. I have tried using online calculators to generate formulas, but they are accurate to 3d.p. at best, which unfortunately isn't any good. I have tried the FORECAST tool in Excel which again, estimates some values below 0.75, when that's clearly where they converge too.
Any ideas? Or even if this is possible. Data points are:
0 0.7894735
0.1 0.7857143
0.3 0.78
0.5 0.77586205
0.75 0.7720588
1 0.7692306
1.5 0.7653061
2 0.762712
3 0.759494
4 0.757575757
5 0.7563025
6 0.7553956
7 0.754717
8 0.75419
9 0.753769
11 0.753138
13 0.752688
15 0.752351
19 0.7518795
29 0.7512519
39 0.7509388
49 0.7507508
99 0.75037517
249 0.75015001
999 0.7500375
Many Thanks
On the off chance that this is still useful, I've found a formula that describes that data set very accurately, to at least six decimal places: $$f(x)=\frac{0.0375003}{x+0.950011}+0.75$$ I used Desmos to find that formula, and you can check out what I did here. In cell 8, you can see that the greatest amount by which this formula's prediction differs from the data is about $3\times10^{-7}$.