A certain medication breaks down in the bloodstream so that 90\% of the initial dosage remains 5\,hours after administration. The amount C(t) of the medication present t hours after the dose is given satisfies dtdC=kC.
(a) Determine the exact value of the decay constant k.
(b) Compute the half\textendash life of the medication, giving both an exact expression and a decimal approximation correct to two decimal places.
(c) How long, to the nearest minute, will it take for only 2\% of the initial dosage to remain in the bloodstream?