Using the Padé  equation to interpolate standard curves

Standard curves often start out linear, but then begin to plateau. Some people fit these to second-order polynomial equations, others to rectangular hyperbola equations. Another choice is the Padé approximant equation.  Actually "Padé " describes a family of equations, with various number of terms in the numerator and denominator. The simplest is the "Padé (1,1)" equation, which only has one term in the numerator (a parameter times X, but no terms with X², X³, etc.) , and one term in the denominator. The Padé (1,1) equation is:

When used to fit a standard curve, there is no need to interpret the three parameters. All you care about is that a smooth curve goes near your standard curve points.

Prism can easily fit this curve using nonlinear regression. It is not a built-in equation (yet; let us know if you think it should be), but can easily be entered as a user-defined equation. Finding rules for initial values can be difficult, but this equation often seems to fit fine when all the initial values are set to 1.0. If the nonlinear regression doesn't converge, you may want to try other values. Let us know if you can think of a useful rule for initial values. 

Here is a graph of a fit from Prism:

Download the Prism file.  You can use it as a template. Or bring up the nonlinear regression parameters dialog, and then the equation editing dialog, and OK from both. Now the equation will be in your list of user-defined equations.