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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 172

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

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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