I've been working on a personal project, and I've come up with a problem that I'm not sure how to proceed on. Here's the issue:

I need a way to determine the value of value Y given the value X for the values X that are not provided. There are different base values for Y, and so I'm trying to develop a formula to reach points associated with X=2 and X=100, with X=60 being a value equal to 40% of the distance between values 2 and 100. I want this to be a gradual curve, with the exact values for X=2 and X=100, rather than a rough estimate such as can be found from a trendline. There were two approaches I attempted - first being Binomial, but my only method is a trendline formula from microsoft excel, and it doesn't hit the most important values exactly. Second attempt was a Power trendline, but the rough intended curve I tried to get just didn't work. I tried doing a compound interest equation next, but it made the resulting values unusable.

But all I want is just a gradual curve, hitting the exact points for values X=2 and X=100, and having X=60 being roughly 40% between the two. Again, I'm not too picky on that, but... how would I guarantee the intersections, while being able to tweak the curve itself? I still think Binomial may be the best approach, but I'm only halfway through my college algebra class and it's entirely possible that my approach to this problem is wrong.

Values less than 2 and greater than 100 don't really matter for this, and the formula I apply for set Y1 I'd want to apply to all other sets, so having this written in a way that I can specify cells in a spreadsheet for the Y coordinates would be ideal.

My apologies if this is confusing, I have difficulties when it comes to communication. If you need me to clarify something, ask and I'll do my best to answer.

Thanks for the help.