Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t) decreases at a rate that is proportional to the amount of the drug that is present at the time. Thus C"(t) = - kC(t), where is a positive number called the elimination constant of the drug.
(a) If C0 is the concentration at time t = 0, find the concentration at time t.
(b) If the body eliminates half the drug in 30 hours, how long does it take to eliminate 90% of the drug?