The exponential function is its own integral (and derivative). Unique among all functions.
Radioactive decay — Total atoms decayed over time.
Population biology — Cumulative growth in populations.
Finance — Continuous compounding total interest.
Heat transfer — Temperature change over time.
Pharmacology — Drug accumulation in body.
Chemistry — Total product formed in first-order reactions.
Electronics — Capacitor charging in RC circuits.
Epidemiology — Total infections in exponential phase.
Physics — Work done against exponential forces.
Machine learning — Softmax normalization constants.
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