A rule for an example of a nonlinear function that fits the following description. when d is 4, r is 9, and r is a function of d

Some possibilities:

r = (9√d) / 2, so f (d) = (9√d) / 2

r = 9d^2/16, so f (d) = 9d^2/16

r = 9 (2^d) / 16, so f (d) = 9 (2^d) / 16

These are examples of non-linear functions of d which fit the description. I think that is what you are asking, but comment if I'm wrong?