- how the y-value should tend to a limit as the distance approaches the radius (quadratically? hyperbolically? exponentially? linearly?.

- Should the function be continuous or discontinuous at the exact radius point.

- What should be the slope of the curve at that point? (or the slope as it tends to it on either side if the function should be discontinuous)

- How should the y-value decay to 0 as distance tends to infinity (same options as my first question.

Update: I'll rephrase this all in plainer English:-

If you were to draw a 2-D graph of this with x is distance on the horizontal axis and y is boost on the vertical axis, and that graph represents a function f, so that y=f(x), there will be a starting value for boost where distance is 0 let's say Z = f(0). From your description, this should decay firstly to f(R), so f(R) < Z. After that it drops more rapidly towards zero. So to describe an example formula for f(x), a mathematician needs to know the shape of the curve before and after the point x=R and whether the point at x=R is smooth or a corner or whether it jumps to a different value at that point (otherwise known as a point of discontinuity). Given this information it then possible to translate the function into Perl.