The concentration of a specific reactant in a chemical solution, C C\,C mg/L, t t\,t hours after the reaction starts, is modelled by the equation:
C=250e−0.12t+15,t≥0 C = 250e^{-0.12t} + 15, \quad t \ge 0 C=250e−0.12t+15,t≥0Determine the initial concentration of the reactant.
Sketch the graph of C C\,C against ttt. On your sketch, state the equation of any asymptote to the curve.
Find the value of t t\,t for which the concentration is 80 mg/L, giving your answer to 2 decimal places.
Show by differentiation that
dCdt=A+BC \frac{dC}{dt} = A + BC dtdC=A+BCwhere A A\,A and B B\,B are constants to be found.
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.
