The concentration of a cleaning agent, CCC grams per litre, in a mixing tank at time ttt minutes after the supply is activated is modelled by the differential equation
dCdt=R−0.15C \frac{dC}{dt} = R - 0.15C dtdC=R−0.15Cwhere RRR is a constant. Initially, the tank contains pure water.
Solve the differential equation to show that C=R0.15(1−e−0.15t)C = \frac{R}{0.15}(1 - e^{-0.15t})C=0.15R(1−e−0.15t).
In the long term, the concentration of the cleaning agent in the tank approaches 40 grams per litre.
Find the value of RRR.
Find the time, in minutes, for the concentration to reach 25 grams per litre, giving your answer to 2 significant figures.
