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.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
