SOLUTION: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 20 minutes, 4.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass

Question 586549: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 20 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 20 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.
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A(t) = ab^t
----
4.25 = 14*b^20
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b^20 = 4.25/14
b = (4.25/14)^(1/20)
b = 0.9421
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Equation:
A(t) = a*0.9421^t
---
Solve for "t":
2 = 14*0.9421^t
----
0.9421^t = 2/14 = 1/7
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Take the log:
t = log[1/7]/log[0.9421] = 32.65 minutes
Visit should be for at least 32.65 minutes
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Cheers,
Stan H.
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