Key concepts: Derivation of exponential decay

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:

Y=Y0*exp(-k*X)

The function exp() takes the constant e ( 2.718...) to the power contained inside the parentheses.