19.3.3—Equations of the form x = x0 e–(t / RC) where x could represent current

A discharging quantity follows x=x₀e^(−t/RC); charging voltage follows V=V₀(1−e^(−t/RC)). Current and charge use the corresponding variable x.

At t=0 and after several τ, use limiting values to check the expression and identify whether the curve rises or falls.

After t=τ in a discharge, voltage and charge are 37% of their initial values; after about 5τ they are close to zero.

The exponent is dimensionless, so t and RC must have the same time units; exponential decay is not linear.