The accumulation factor R increases as the dosing interval tau becomes shorter, assuming constant k.

• A. R decreases as tau decreases.
• B. R increases as tau decreases.
• C. R is independent of tau.
• D. R becomes zero as tau decreases.

Answer: (B)

Accumulation happens because with repeated dosing the drug isn’t fully cleared before the next dose. For first‑order elimination the steady‑state accumulation factor is R = 1 / (1 − e^(−kτ)), where k is the elimination rate constant and τ is the dosing interval. As the dosing interval gets shorter, kτ gets smaller, so e^(−kτ) gets closer to 1 and the denominator 1 − e^(−kτ) becomes smaller. That makes R larger, meaning more drug accumulates with each dose. In the extreme, as τ → 0, R tends toward infinity, reflecting continuous dosing with essentially no time to eliminate. Conversely, as τ grows large, R approaches 1, indicating little to no accumulation. For a quick sense of numbers, if k = 0.1 h^−1, a 12-hour interval gives R ≈ 1.43, while a 6-hour interval gives R ≈ 2.22.