Why is a half-life an exponential function?

A half-life is an exponential function because it describes the process of decay or growth at a constant rate over time. In a half-life scenario, the quantity decreases by half in each fixed time interval, which results in a rapid initial decrease that slows over time. This behavior follows the mathematical form of an exponential decay function, where the quantity remaining can be expressed as a constant multiplied by an exponential term. Consequently, the relationship between time and quantity is characterized by a consistent percentage decrease, leading to the characteristic curve of exponential functions.