Chapter 5.3, Problem 87E

Drug concentration. A single injection of a drug is administered to a patient. The amount Q in the body then decreases at a rate proportional to the amount present. For a particular drug, the rate is 4% per hour. Thus,

     $\frac{dQ}{dt}=-0.04QQ(0)=Q_0$

where t is time in hours.

(A)    If the initial injection is 5 milliliters [Q(0) = 5], find Q = Q(t) satisfying both conditions.

(B)    How many milliliters (to two decimal places) are in the body after 10 hours?

(C)    How many hours (to two decimal places) will it take for only 1 milliliter of the drug to be left in the body?