a) A certain radioactive material is known to decay at a rate proportional to the amount present. If after two hours it

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A A Certain Radioactive Material Is Known To Decay At A Rate Proportional To The Amount Present If After Two Hours It 1 (57.83 KiB) Viewed 28 times

a) A certain radioactive material is known to decay at a rate proportional to the amount present. If after two hours it is observed that 15% of the material has decayed, find the half-life of the radioactive material. b) c) A tank contains 50 litres of solution containing 4 grams of substance per litre. A liquid solution containing 6 grams of this substance per litre runs into the tank at the rate of 5 litre/minute and the well-stirred mixture runs out of the tank at the same rate. (1) (ii) (iii) Model this situation by a differential equation with initial conditions. Find the amount of substance in the tank after 20 minutes. Find the limiting amount of substance in the tank. (Hint: The limiting value will be as time goes to infinity.) Use power series to find the general solution of y" - 2xy' + (x + 2)y = 0.