A group of patients is given a certain dose of a drug once. The patients eliminate the drug at a steady rate. Two measurements of the drug concentration in the blood are taken 24 hours apart to determine the rate at which the drug is removed from the blood stream. The measurements are given below.

patient	initial measurement (t=0)	measurement after 24 hours
1	0.20.2	0.040.04
2	0.50.5	0.10.1
3	0.60.6	0.120.12
4	0.90.9	0.180.18

a)Find the value ofaathat will give a DTDS of the formxt+1=axtxt+1=axtfor the drug removal, wherettis in days. Expressaaas a simple fraction.

Answer:a=a=__________

b)For patient 4, assuming elimination at a continuous rate, exactly how long will it take until the drug concentration is below or equal to0.010.01? Give your answer with an accuracy of at least two decimal points.

Answer: ____________days

c)Exactly how long does it take for the initial concentration to decrease by5050%? Give your answer with anaccuracy of at least two decimal points.

Answer:____________ days

d)Supposepatients are now given a dosebbevery 24 hours; namely, we have the DTDSxt+1=axt+bxt+1=axt+b, whereaais the value found in part (a) above. How large should this dose be in order for the steady state concentration to be3/53/5? Give an exact answer, not a decimal.

Answer:b=b=__________