Define X to be time, and Y to be the outcome you are measuring. Three examples:
•Number of ligand-receptor complexes still present -- the ligand has not yet dissociated.
•The number of radioactive atoms that have not yet decayed.
•The concentration of drug in the plasma, not yet metabolized.
At any given time X. The rate of change of Y is proportional to Y. Expressed as a differential equation:
Shown as a graph:
When you integrate both sides of the equation, you get the equation for exponential decay:
The function exp() takes the constant e ( 2.718...) to the power contained inside the parentheses.