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Question 430

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≥0
a.

Find the initial concentration of the contaminant in the sample.

[1]
b.

Sketch the graph of C C\,C against hhh. On your sketch, state the equation of any asymptote to the curve.

[3]
c.

Find the value of h h\,h for which C=50C = 50C=50, giving your answer to 2 decimal places.

[3]
d.

Show by differentiation that

dCdh=A+BC \frac{\mathrm{d}C}{\mathrm{d}h} = A + BC dhdC​=A+BC

where A A\,A and B B\,B are constants to be determined.

[3]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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