4. A tank contains 30 litres of a solution of a chemical in water. The concentration of the chemical is reduced by running pure water into the tank at a rate of 1 litre per minute and allowing the solution to run out of the tank at a rate of 2 litres per minute. The tank contains x litres of the chemical at time t minutes after the dilution starts. dx -2x a) Show that dt 30-t b) Find the general solution of this differential equation. c) Find the fraction of the original chemical still in the tank after 20 minutes. C

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