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 be the number of kilograms of chemical that remains dissolved in the spa pool after minutes. The differential equation relating to t is

A tank initially contains 300 grams of salt that is dissolved in 50 L of water. A solution containing 15 grams of salt per litre of water is poured into the tank at a rate of 2 L per minute and the mixture in the tank is kept well stirred. At the same time, 5 L of the mixture flows out of the tank per minute.

A differential equation representing the mass, grams, of salt in the tank at time minutes, for a non-zero volume of mixture is

Water containing 2 grams of salt per litre flows at the rate of 10 litres per minute into a tank that initially contained 50 litres of pure water. The concentration of salt in the tank is kept uniform by stirring and the mixture flows out of the tank at the rate of 6 litres per minute.

If grams is the amount of salt in the tank minutes after the water begins to flow, the differential equation relating to is

A.  

B.  

C.  

D.  

E.  

A large tank initially holds 1500 L of water in which 100 kg of salt is dissolved. A solution containing 2 kg of salt per litre flows into the tank at a rate of 8 L per minute. The mixture is stirred continuously and flows out of the tank through a hole at a rate of 10 L per minute.

The differential equation for , the number of kilograms of salt in the tank after minutes, is given by

A.   

B.  

C.  

D.  

E.  

A tank initially holds 16 L of water in which 0.5 kg of salt has been dissolved. Pure water then flows into the tank at a rate of 5 L per minute. The mixture is stirred continuously and flows out of the tank at a rate of 3 L per minute.

1.  Show that the differential equation for , the number of kilograms of salt in the tank after minutes, is given by
2.   (1 mark)
   

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2. Solve the differential equation given in part a. to find as a function of .
3. Express your answer in the form  , where and are positive integers.  (3 marks)
   

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