What is exponential?

Processes follow exponential models when the rate at which something is happening depends on the amount that is present.

Exponential dissociation vs. association vs. growth

The dissociation model always heads downhill gradually approaching a plateau.

The association model always heads uphill, and also approaches a plateau.

The growth model goes up and up and up, getting steeper, never reaching a plateau.

Rate constants vs. time constants vs. half-lives

In all the exponential models, one (or more in some cases) parameter describes how rapidly the process occurs. It can be expressed as a rate constant (in units of inverse time) or as a time constant (in units of time), or as a half-life, also in units of time.

The rate constant and time constants are simply reciprocals of each other. Prism always fits the rate constant (k), but computes the time constant (tau) as well and reports the standard error and confidence interval of the time constant just as if the model had been written to fit that constant.

The half-life equals ln(2)/k where ln is the abbreviation for natural logarithm.