When Does a Towel Stop Drying and Start Seeding? A Reuse Interval from Drying and Growth Curves

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. In the ventilated case the towel fell below the growth threshold in 5 hours and could serve 6 daily uses before crossing the ceiling, corresponding to a 6 day interval. In the still humid bathroom it needed 13 hours to leave the growth zone and crossed the ceiling after 3 uses, a 3 day interval at daily use. Twice-daily use shortened the humid interval to 2 days while barely changing the ventilated one. Laundering on the conditional rule cost 74 loads per towel per year against 52 for a flat weekly wash, with the humid-room towel, not the ventilated one, driving the extra washes. The proposed arrangement is as follows. The proposed rule is conditional rather than flat: a towel that dries fully between uses may serve for the longer derived interval, while a towel in a humid room is retired sooner or, better, moved to dry where air moves. The cheapest intervention in the whole study is a hook by a window or door in place of a bar behind the bathroom door, and its effect is quantified as a change in drying time constant. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.