Is this problem solvable?

From: Michael (mkoss917_at_yahoo.com)
Date: 06/29/04 

Date: 29 Jun 2004 12:40:58 -0700

I have a problem I am not sure is solvable. There is an unknown
formula that calculates a value based on 10 parameters. Of these 10
parameters, 1 is an integer and the other 9 are fractional. For
example:

a = 18, b = 6.5, c = 2.7, d = 3.2, e = 6.4, f = 9.2, g = 1.1, h = 3.8,
i = 5.0, j = 3.1

f(a,b,c,d,e,f,g,h,i,j) = 3010

I have about 20,000 data points of a,b,c,d,e,f,g,h,i = x. There's a
catch, though. The only data I am allowed to see is integer values for
each variable. For example:

18 6 2 3 6 9 1 3 5 3 = 3010

I believe the formula used to calculate x is exponential because
higher variables tend to produce significantly higher values. Also, I
know that b and c are weighted more than the other variables, and a
and j are weighted very little, if at all. Also, most of my 20,000
data points have b = 6 and f = 7.

What I would like to figure out is a method to determine the
fractional part of each variable. Really, if I could only find the
fractional value of f, that would be fine too. So given the input:

18 6 2 3 6 9 1 3 5 3 = 3010

I would like to be able to figure out that f = 9.2. I realize there
probably isn't a way to find the fractional values with 100%
confidence, but if I knew with 95% confidence that 9.1 <= f <= 9.3,
that would be sufficient.

Is this problem solvable? If so, what methods should I use? I am not
looking for someone to do this work for me, but rather to guide me in
finding an answer. I haven't taken many advanced math classes, but I
am willing to do research. I just don't know what method(s) to
research. Feel free to email any questions to mkoss917 {at} yahoo
(dot) c-o-m.

Thanks for any help you may provide,

Michael.