The amount of drug in patient's bloodstream, A(t), t hours after an intravenous infusion begins can be modeled by A(t) = R -(1 - ekt) -k where r is the rate of infusion per hour and k is the exponential constant for the drug. A(t), t hours after an intravenous infusion begins can be modeled by A(t)=(1- -(1-ekt) where r is the rate of infusion per hour and k is the exponential constant for the drug. [a.] Is A(t) an exponential decay function or an exponential growth function? Explain your reasoning Your Answer: [b.] Now, let's take a look the same drug that is used for the control of blood pressure in patients with severe hypertension. Suppose that this drug is given to the patient by intravenous infusion at a drip rate of 6mg/h. Recall that the half-life of this drug is 4 hours. Find a model for the amount of drug in patient's bloodstream t hours after the drug is administered (Round (r/-k) to a whole number), sketch the graph of A(t) using a computer, and find a horizontal asymptote for A(t). Your Answer: [c.] Find the average rate of change of drug in patient's bloodstream between t t = 0. Repeat it for t = 4 and t = 6. (In all calculations, round to 2 decimal places.) Your Answer: 2 and [e.] What happens to the amount of drug in patient's bloodstream after a long period of time? (i.e. What is the limit of the function as t approaches to co?) Your Answer: