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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 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]

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

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