After two time constants, approximately what percentage of lung unit filling is achieved?

• A. 63%
• B. 86%
• C. 95%
• D. 98%

Answer: (B)

Lung unit filling follows an exponential approach to its final volume, governed by a time constant τ. After a time equal to two of these constants, the fraction filled is 1 minus e to the power of negative two, which is 1 − e^(-2) ≈ 0.8647, about 86%. So roughly 86% of the lung unit has filled after two time constants. This also fits the familiar milestones: about 63% after one τ, about 95% after three τ, etc.