Exponential response
Also: exponential curve
A change whose rate is proportional to its remaining distance from a limit.
First-order homogeneous dynamics produce e^(−t/τ); equal time intervals multiply the remaining error by a constant factor.
- Formula
x(t) = x∞ + (x₀−x∞)e^(−t/τ)
Example After 3τ, a decay retains about 5% of its initial value.
Common misconception Exponential decay approaches zero asymptotically rather than subtracting a fixed amount each second.