Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. This means the larger the quantity, the faster it decreases, and as it gets smaller, the rate of decrease slows down. It’s commonly modeled by the equation:

$N(t) = N_0 e^{-\lambda t}$

where:

• $ N(t) $ is the amount at time $ t $,

• $ N_0 $ is the initial amount,

• $ \lambda $ is the decay constant,

• $ e $ is Euler’s number (approximately 2.718).

Exponential decay appears in many natural and scientific contexts, such as radioactive decay, cooling of objects, and depreciation of assets. A key feature is the “half-life,” the time it takes for the quantity to reduce to half its original value. This process never truly reaches zero but gets infinitely close over time. The curve of exponential decay is steep at first and gradually flattens, forming a smooth, downward-sloping curve.