The sleeping aid Ambien has a biological half-life of about 1.5 hours. Assume someone takes a 10 mg dose at 9:00 p.m.
(a) Find an exponential model for the amount of Ambien in the person's body x hours after 9:00 p.m.
(b) What is the decay rate?
(c) How much Ambien will be left at 10:00pm?
(d) Estimate how long it takes for amount of Ambien to reach 2 mg.