The concentration, CCC mg/L, of a particular chemical residue in a large processing tank, ttt hours after a neutralising catalyst is introduced, is modelled by the differential equation
dCdt=−k(C−10)2 \frac{\text{d}C}{\text{d}t} = -k(C - 10)^2 dtdC=−k(C−10)2where kkk is a constant and C>10C > 10C>10.
Given that the concentration of the residue:
Solve the differential equation to show that, according to the model
C=at+bct+d C = \frac{at + b}{ct + d} C=ct+dat+bwhere a,b,ca, b, ca,b,c and ddd are integers to be found.
Hence find, according to the model, the time taken for the concentration of the residue to fall to 404040 mg/L. Give your answer to the nearest hour.
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.
