This may seem like basic math, but I'm trying to determine the relationship between the following sets of numbers to understand how they scale. I would like to write an equation to output y when given x, as follows:
when x = 1366, y = 4.67
when x = 1700, y = 5.0
when x = 2106.45, y = 5.33
I would like an equation that generates the y above when given x, in the context of the relationship between these numbers. I'm stumped.
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I explored logarithmic functions but wasn't able to come up with anything, and the only constant I was able to solve for was 1.16237188872621, which appears to be the factor by which the ratio between x and y here increments by... e.g.
1366 / 4.67 = 292.5053533191
1700 / 5.0 = 340
2106.45 / 5.33 = 395.2063789869
292.5053533191 * 1.16237188872621 = 340
340 * 1.16237188872621 = 395.2063789869
...and so on. Thanks for any help with this!
For example: $$y=\frac{(x-1700)(x-2106.45)}{(1366-1700)(1366-2106.45)}\cdot4.67+\frac{(x-1366)(x-2106.45)}{(1700-1366)(1700-2106.45)}\cdot5.0+$$ $$+\frac{(x-1366)(x-1700)}{(2106.45-1366)(2106.45-1700)}\cdot5.33.$$