Decay Curve

The decay curve N(t) = N₀ e^(−λt) is an exponential drop.

It looks STRAIGHT on a semi-log plot (ln N vs t): slope = −λ, intercept = ln N₀.

Half-lives evenly space along t-axis: at T_½, 2T_½, 3T_½, … the count halves each time.

Tail of the curve never reaches zero (exponentials are asymptotic) — but after many T_½ the count is negligibly small.

Daughter accumulation in a chain (Parent → Daughter): daughter builds up to a maximum, then decays if it too is unstable.

Secular equilibrium: when parent is much longer-lived than daughter, daughter activity equals parent activity at equilibrium.

Transient equilibrium: parent slightly longer than daughter; daughter exceeds parent for a while before equilibrium.