SOLUTION: During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is admin

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Question 1131149: During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is administered is given by the following.
T(t) = 70(0.727)t
(a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 20 minutes after the anesthetic is administered_______mg
b) How long, to the nearest minute, can the operation last if the patient does not receive additional anesthetic?_______min
Answer by MathLover1(20850) About Me  (Show Source):
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During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is administered is given by the following.

T%28t%29+=+70%280.727%29%5Et
(a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system t=20 minutes after the anesthetic is administered_______mg
20 minutes is (1/3) hour, so evaluate T for t=(1/3)
T%281%2F3%29+=+70%280.727%29%5E%281%2F3%29
T%281%2F3%29+=+70%2Aroot%283%2C0.727%29
T%281%2F3%29+=+70%2A0.899176
T%281%2F3%29+=+62.94232
to the nearest milligram:
T%281%2F3%29+=+63mg

b) How long, to the nearest minute, can the operation last if the patient does not receive additional anesthetic?_______min
63+=+70%280.727%29%5Et
63%2F+70=%280.727%29%5Et
0.9=%280.727%29%5Et
log%280.9%29=log%28%280.727%29%5Et%29
log%280.9%29=tlog%280.727%29
t=log%280.9%29%2Flog%280.727%29
t=0.330461 hours
t=0.330461hours%2A+60+%28min%2Fhour%29
t=19.8277min=> t=20min