Question 1113350: I have worked this problem out several time and keep getting the same answer of 68 mg and 88 minutes. However it keeps saying I am wrong. Here is the problem:
During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 100 milligrams of anesthetic is administered is given by the following.
T(t) = 100(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
Found 2 solutions by math_helper, Boreal:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! I have worked this problem out several time and keep getting the same answer of 68 mg and 88 minutes. However it keeps saying I am wrong. Here is the problem:
During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 100 milligrams of anesthetic is administered is given by the following.
T(t) = 100(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?
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There is a problem with the formula T(t) = 100(0.727)t
… at t=0 it gives you 0 mg, and then goes UP from there
...
Please correct and re-post.
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Ok, so its 
a) 20min must be converted to hours, because the equation wants t in units of hours:
20min = 20min*1hr/60min = 1/3 hr
T(20min) = T(1/3 hr) =  , rounded:  mg
b) 50mg is the threshold, so we're looking for t when the T(t) reaches 50mg:
T(t) = 
 hours =  min
Rounded to the nearest minute:  min
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! 20 minutes is 1/3 hour.
t(1/3)=100*(0.727)^(1/3)=100*0.8992=89.92 or 90 minutes
50=100*0.727^t
0.5=0.727^t
ln both sides
-0.693=t ln (0.727)
t=-0.6931/-0.3188
=2.17 hours or 2 hours 10 minutes
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