The concentration of a specific chemical, CCC mmol/L, in a bioreactor ttt hours after a growth process starts is modelled by the differential equation
dCdt=α−0.25C \frac{dC}{dt} = \alpha - 0.25C dtdC=α−0.25Cwhere α\alphaα is a positive constant. At the start of the process, there is no trace of the chemical in the reactor.
Solve the differential equation to show that C=4α(1−e−0.25t)C = 4\alpha(1 - e^{-0.25t})C=4α(1−e−0.25t).
In the long term, the concentration in the bioreactor stabilizes at 20 mmol/L.
Find the value of α\alphaα.
Determine the time, in hours, for the concentration to reach 15 mmol/L, giving your answer to 2 significant figures.
