Finding a Formula with a LINEST() Style-Function for a Curved Line

You can use the LINEST function to return the components of a polynomial trendline

So the main goal is to get a formula that will more closely represent these points than a LINEST() and give me the y values for the x values I don't have listed. Any help?

The hardest part of this question as I see it isn't really an Excel question at all, and it's probably a question that we on this forum are not going to be able to answer for you. The question boils down to "what kind of equation will give a reasonable best fit?"

A lot of people will try to use polynomials as Andy Pope suggested. We like to use polynomials for several reasons. 1) They are infinitely flexible, which means that, by choosing a higher order polynomial, we can "fit" most data sets. 2) Polynomials are always "linear" (I don't know if your math education extends to linear algebra, but here we are using the term as it is used in linear algebra. In short, this means that "linear" refers to more than just straight lines and that "linear" regression routines like LINEST() will be able to find the parameters for us). 3) The math around polynomials is fairly well understood, a staple of most math classes, which means we are "comfortable" with polynomials.

There are downsides to using polynomials. 1) Because of their flexibility, each term you add increases the potential for stretches where the function is unreasonable. At higher orders, it will certainly not extrapolate reliably, and there could easily be regions where it does not interpolate reliably. For your specific example, it appears that the data approach 0 asymptotically (but y is never <0) as x gets smaller and approach 100 asymptotically as x gets larger. If this is truly how your function should behave, it will likely be very difficult to constrain a polynomial to these limits (y is never <0 and y is never > 100). 2) Polynomials may not provide any insight into the process behind the data.

I think you will be better served to step away from Excel for a while and research what kind of function should be used for the data. One that shows up here occasionally is what users have called a "logistics" function http://en.wikipedia.org/wiki/Logistics_function Logistics functions are fairly common for these kind of S shaped curves and can usually fit the data with fewer parameters than a polynomial. Usually they cannot be made "linear" like polynomials, so the algorithms behind LINEST() will not be able to regress them. You can use Solver, and even automate it to occur automaticallly (though naturally this isn't as convenient as the linear algorithms in LINEST()). If you decide that polynomials are an acceptable solution, you can use Andy Pope's spreadsheet as your starting point. I would suggest that, in the long run, you might be better served to find a better equation form that is better suited to your data.