The "Simple" means that there is only one x variable. y = f(x). So the curve exists in two dimension and can be plotted on screen or sheet of paper. The "non-linear" means that, when we graph the data, it does not roughly follow a straight line, so we must look for an appropriate curve.
The following are probably the most common non-linear curves used:
Exponential and Logarithmic curves have rapid accelerations or decelerations
in the slope. Power curves have a more gradual change. Polynomial functions
can be used for more complex curves, which change direction, as shown in our Tip of the Week for May 17, 2017
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.