### Basic functions: Power functions

### Context 2: Psychophysics

Psychophysics is a context for power functions.

The American psychologist Stanley Smith Stevens has published much material showing that the sensation \(R\) (response) is proportional to a constant power of the stimulus \(S\) (stimulus). **Stevens's power law** is as follows in formula language: \[R=a\cdot S^b\] The values of the parameters \(a\) and \(b\) vary per stimulus (smell, hearing, sight, etc.).

For the perception of light from a point source, for example, one has found \(b=0.5\) and thus one has to do with a multiple of the square root function.

For gustatory perception, use \(b=1.3\) for sucrose (natural sugar) and \(b=0.8\) for saccharin (E954, an artificial sweetener) to link sweetness taste to the stimulus strength. You can use this formula to compute how much saccharin is needed as replacement of sugar in order to have the same sensation of sweetness as sugar, at a given concentration. This is not an unambiguous relationship because of differences in values of \(b\).