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

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Question 22

The concentration of a cleaning agent, CCC grams per litre, in a mixing tank at time ttt minutes after the supply is activated is modelled by the differential equation

dCdt=R−0.15C \frac{dC}{dt} = R - 0.15C dtdC​=R−0.15C

where RRR is a constant. Initially, the tank contains pure water.

a.

Solve the differential equation to show that C=R0.15(1−e−0.15t)C = \frac{R}{0.15}(1 - e^{-0.15t})C=0.15R​(1−e−0.15t).

[5]
b.

In the long term, the concentration of the cleaning agent in the tank approaches 40 grams per litre.

Find the value of RRR.

[2]
c.

Find the time, in minutes, for the concentration to reach 25 grams per litre, giving your answer to 2 significant figures.

[3]

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

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