A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 milligrams of the material present and after two hours it is observed that the material has lost 20% of its original mass, find (a) an expression for the mass of the material remaining at any time , (b) the mass of the material after five hours; and (c) the time at which the material has decayed to one half of its initial mass.

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