Discussion
After a source is switched off in a room with 2 air changes per hour, the concentration falls to \( e^{-1} \) of its initial value in
Answer: B
Correct answer: 30 minutes
After the source stops, the concentration decays exponentially with time constant \( \tau = 1/n \):
\[ \tau = \frac{1}{2} \ \mathrm{h} = 30\ \mathrm{minutes} \]
which is by definition the time to fall to \( e^{-1} \), about 37 per cent, of the initial value. The relation is what a tracer gas decay measurement exploits in reverse: fitting an exponential to the recorded decay gives the slope, and the slope gives the air exchange rate.
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