Expanding on hdb's idea, you could do what I did on a "programming lab" assignment for Analog Circuits: Keep the curve the same, and change the scales to suit.

Granted, there were only 3 types of graphs to draw (overdamped, underdamped, and critically damped), but it was straightforward to determine these. Given the right choice, the time and amplitude axes were scaled to suit.

In the OP, you may be able to setup an equation and solve for the kind of curve. You can do what they do in when developing statistical models, which is throw every kind of term into the model, and see which terms correlate. There are variations where one term at a time is dropped, and the regression rerun. When only one term is left, that is usually the best one. (Though sometimes a polynomial will appear linear and such, but then, it was nearly linear to begin with.)