Five time constants correspond to what percentage of lung volume change?

Five time constants correspond to what percentage of lung volume change?

• A. 63.2%
• B. 86.5%
• C. 95%
• D. 99.3% to 99.8%

Answer: (D)

Five time constants describe how an exponential system approaches its new steady state. In respiratory mechanics, the volume change over time follows V(t) = V_final − (V_final − V_initial) e^(−t/τ), where τ is the time constant. After five constants (t = 5τ), the remaining portion of the change is e^(−5) ≈ 0.0067, so about 0.67% remains to be achieved. That means roughly 99.33% of the volume change has occurred. Since the range given (around 99.3% to 99.8%) matches this, five time constants correspond to about 99.3% of the change.

Five time constants describe how an exponential system approaches its new steady state. In respiratory mechanics, the volume change over time follows V(t) = V_final − (V_final − V_initial) e^(−t/τ), where τ is the time constant. After five constants (t = 5τ), the remaining portion of the change is e^(−5) ≈ 0.0067, so about 0.67% remains to be achieved. That means roughly 99.33% of the volume change has occurred. Since the range given (around 99.3% to 99.8%) matches this, five time constants correspond to about 99.3% of the change.