Given this discrete non-linear set of values how can I get an equation for it?

Question

I want to generate a equation in the form f(x) = {...} for this discrete data below. As X doubles Y halves but its a bit more complicated.

Using an online Polynomial Interpolation calculator I got:

f(x)= (1.0986 * 10^−9 * x^6)− (6.97*10^−7 * x^5) + (0.000146503 * x^4) − (0.012976 * x^3) + (0.519038 * x^2) − (9.37617 * x) +(71.4375)

or (easier to read):

y = 71.4375 - 9.37617x + 0.519038x^2 - 0.012976 * x^3 + 0.000146503 * x^4 - 6.97*10^−7 * x^5 + 1.0986 * 10^−9 * x^6

But although the values mapped, some values of x made y negative as you see here which is wrong.

All I want is a close enough equation for the data but I'm unable to find the right tools or methods inorder to do so.

Thanks

Answer 1

What about $y= \frac{180}{x}$?