The Amount of Medicine in the Bloodstream Decays Exponentially with a Half-Life

Short Answer

The amount of medicine in the bloodstream decays exponentially with a half-life of 4 hours. There must be at least 25 milligrams of medicine per pound of body weight to keep the patient safe during a one-hour procedure.
Set up an initial value problem whose solution is the amount of medicine, x(t) (measured in milligrams), in the bloodstream at time t. Let t = 0 correspond to the time when the procedure begins, and assume that x(0) = x₀. Determine the exact value of proportionality constant in the differential equation from.