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Question 563

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≥0
a.

Determine the initial concentration of the reactant.

[2]
b.

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

[2]
c.

Find the value of t t\,t for which the concentration is 80 mg/L, giving your answer to 2 decimal places.

[3]
d.

Show by differentiation that

dCdt=A+BC \frac{dC}{dt} = A + BC dtdC​=A+BC

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

[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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