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11.11 Modelling with Differential Equations

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Question 13

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]

11.11 Modelling with Differential Equations Questions

  1. A Level
  2. /Maths
  3. /11.11 Modelling with Differential Equations

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.

Question bank