Specialist2023 Exam 2 Section A · Q8CAS active1 mark

Differential equation for chemical in a spa pool

Initially a spa pool is filled with 8000 litres of water that contains a quantity of dissolved chemical. It is discovered that too much chemical is contained in the spa pool water. To correct this situation, 20 litres of well-mixed spa pool water is pumped out every minute while 15 litres of fresh water is pumped in each minute.

Let $Q$ be the number of kilograms of chemical that remains dissolved in the spa pool after $t$ minutes.

The differential equation relating $Q$ to $t$ is

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\dfrac{dQ}{dt} = \dfrac{4Q}{t - 1600}

\dfrac{dQ}{dt} = \dfrac{-Q}{400}

\dfrac{dQ}{dt} = \dfrac{3Q}{t - 1600}

\dfrac{dQ}{dt} = \dfrac{3Q}{1600 - t}

\dfrac{dQ}{dt} = \dfrac{4Q}{1600 - t}

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