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The steady-state approximation (hereafter abbreviated as SSA) consists insetting $dy/dt=0$, where $y$ denotes the concentration of a short-livedintermediate subject to first-order decay with a rate constant $k$. The solereason for enforcing SSA is to convert the rate equation for $y$ into analgebraic equation. The conditions under which SSA becomes trustworthy are nowwell understood, but a firm grasp of the physical content of the approximationrequires more maturity than few teachers, let alone their students, may beexpected to possess. Furthermore, there is no simple way to gauge the accuracyof the results derived by imposing SSA. The purpose of this note is todemonstrate that a better, but equally simple, approximation results if,instead of setting $dy/dt$ to zero, one substitutes $y(t+\tau)$ for $y+\taudy/dt$, where $\tau=1/k$; SSA is a cruder approximation because it neglects thesecond term. For systems modelled as damped harmonic oscillators, the "reverseTaylor approximation" can be extended by retaining one more term in the Taylorexpansion. The utility of the approximation (or its extension) is demonstratedby examining the following systems: radioactive equilibria, Brownian motion,dynamic response of linear first- and second-order systems.

A Superior but Equally Convenient Alternative to the Steady-State Approximation and Secular Equilibrium