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 11.11 Modelling with Differential Equations with exam-style questions for A Level Maths. 51 questions, 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.
