The concentration of a specific contaminant in a groundwater sample, C C\,C mg/L, h h\,h hours after a purification agent is added, is modelled by the equation
C=250e−0.12h+15,h≥0 C = 250e^{-0.12h} + 15, \quad h \ge 0 C=250e−0.12h+15,h≥0Find the initial concentration of the contaminant in the sample.
Sketch the graph of C C\,C against hhh. On your sketch, state the equation of any asymptote to the curve.
Find the value of h h\,h for which C=50C = 50C=50, giving your answer to 2 decimal places.
Show by differentiation that
dCdh=A+BC \frac{\mathrm{d}C}{\mathrm{d}h} = A + BC dhdC=A+BCwhere A A\,A and B B\,B are constants to be determined.
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.
