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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 215

The concentration of a specific chemical, CCC mmol/L, in a bioreactor ttt hours after a growth process starts is modelled by the differential equation

dCdt=α−0.25C \frac{dC}{dt} = \alpha - 0.25C dtdC​=α−0.25C

where α\alphaα is a positive constant. At the start of the process, there is no trace of the chemical in the reactor.

a.

Solve the differential equation to show that C=4α(1−e−0.25t)C = 4\alpha(1 - e^{-0.25t})C=4α(1−e−0.25t).

[5]
b.

In the long term, the concentration in the bioreactor stabilizes at 20 mmol/L.

Find the value of α\alphaα.

[2]
c.

Determine the time, in hours, for the concentration to reach 15 mmol/L, giving your answer to 2 significant figures.

[3]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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