The function C(t) = K(e^-at - e^-bt), where a, b, and K are positive constants and b > a, is used to model the concentration at time t of a drug injected into the bloodstream.
(a) Show that lim_t→∞ C(t) = 0.
(b) Find C'(t), the rate of change of drug concentration in the blood.
(c) When is this rate equal to 0?