So let us say that there is time variable $t$ that can only be natural number. And then, for each $t$ there are data for each variable $a$, $b$, $c$, and so on. And then we have variable $y$. We want to express $y$ in term of $a$,$b$,$c$ and other variables. The equation does not have to be linear and it can be non-linear. In such case, assume that function only has to fit data points and for $t$ that has not been reached, things can be extrapolated.
So if we have data points for each variable, then what would be the number of functions that would fit perfectly to form a function that maps from domain variables to $y$?
what would be the minimum and maximum bound on the number of possible functions as data are added to every variable and therefore $t$ increases - not just when $t \to \infty$ but how this will change depending on $t$?
Every variable is real number variable.