Exponential (Function)
Definition
Growth or decay where the rate is proportional to the current amount — the mathematics of radioactivity, charging capacitors, and pandemics.
Technical definition
Functions of form f(t) = A·e^(kt): k > 0 gives growth, k < 0 decay. Characterized by constant doubling/halving time. Solutions to dy/dt = ky — the most common differential equation in physics (RC circuits, radioactive decay, cooling).
Example
Radioactive decay: after each half-life, half remains — the exponential N = N₀e^(−λt) describes every nucleus from carbon-14 to uranium-238.
Common confusion
‘Exponential growth’ does not mean ‘very fast’ — it means proportional growth, which starts slow. Early outbreak curves looked flat precisely because exponentials start deceptively small.