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1.9.31 Formulate first order differential equations (A-level only)

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Question 13

The concentration of a specific reactant in a chemical solution, $C\,$ mg/L, $t\,$ hours after the reaction starts, is modelled by the equation:

250e^{-0.12t} + 15, \quad t \ge 0

Determine the initial concentration of the reactant.

[2]

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

[2]

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

[3]

Show by differentiation that

\frac{dC}{dt} = A + BC

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

[3]

Markscheme

1.9.31 Formulate first order differential equations (A-level only) Questions

A Level
Maths
1.9.31 Formulate first order differential equations (A-level only)

50 exam-style questions on OCR (MEI) A Level Maths 1.9.31 Formulate first order differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.9.31 Formulate first order differential equations (A-level only)

Question bank

1.9.31 Formulate first order differential equations (A-level only)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Question 13

The concentration of a specific reactant in a chemical solution, $C\,$ mg/L, $t\,$ hours after the reaction starts, is modelled by the equation:

250e^{-0.12t} + 15, \quad t \ge 0

Determine the initial concentration of the reactant.

[2]

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

[2]

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

[3]

Show by differentiation that

\frac{dC}{dt} = A + BC

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

[3]

Markscheme

1.9.31 Formulate first order differential equations (A-level only) Questions

A Level
Maths
1.9.31 Formulate first order differential equations (A-level only)

50 exam-style questions on OCR (MEI) A Level Maths 1.9.31 Formulate first order differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.