At noon, the outdoor concentration of a certain pollutant is 120 parts per billion…
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
At noon, the outdoor concentration of a certain pollutant is 120 parts per billion (ppb) and decays according to the law O(t)=120e−0.040t, where t is measured in minutes after noon. An indoor air freshener releases a fragrance whose concentration in the room is modeled by F(t)=5e0.070t ppb for the same time interval.
(a) Solve for the time t>0 (in minutes) at which the concentrations of pollutant and fragrance are equal. Round your answer to the nearest tenth of a minute.
(b) Evaluate the instantaneous rates of change O′(t) and F′(t) at the time found in part (a). Interpret the signs of these derivatives in context.
(c) Compute the pollutant concentration 15 minutes after the time found in part (a) and state whether the pollutant remains the dominant component of the room air at that moment.