Question 416066: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 24 minutes, 4.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You go to the doctor and he gives you 14 milligrams of radioactive dye.
After 24 minutes, 4.25 milligrams of dye remain in your system.
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A(t) = ab^t
4.25 = 14b^24
b = (4.25/14)^(1/24) = 0.9515
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Solve for "t" if:
2 = 14^t
[0.9515]^t = 1/7
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Take the log to solve for "t":
t*ln[0.9515] = ln[1/7]
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t = -1.9459/-0.04972
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t = 39.14 minutes (this is when he will have 2ml in his blood)
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Ans: More than 39.14 minutes.
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Cheers,
Stan H.
To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
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