singleexponential

Singleexponential refers to a functional form described by a single exponential term, often written as f(t) = A e^{-t/τ} or f(t) = A e^{-λ t}, describing processes with a constant fractional rate. It contrasts with multi-exponential models that combine several exponentials to capture multiple time scales.

Properties: For A > 0, the function decreases monotonically with t, approaching zero as t → ∞. The initial value is f(0) = A. The time constant τ = 1/λ governs the rate; the half-life t1/2 = τ ln 2.

Applications: Widely used in physics and chemistry to model radioactive decay and first-order reaction kinetics. In biology and medicine, it describes plasma clearance in pharmacokinetics and fluorescence decay. In signal processing, it models envelopes of damped signals. Parameters A and τ or λ are estimated from data via regression on the semi-log plot: ln(f) vs t yields a straight line with slope -1/τ or -λ.

Limitations: Real systems may exhibit multiple processes; if data deviate from a single linear trend in semi-log space, a multi-exponential or non-exponential model may be more appropriate. Variants include time-varying rates and stretched exponentials.