Question

You go to the doctor and he gives you 12 milligrams of radioactive dye. After 20 minutes, 7 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?

Answer 1

34.12 minutes

Step-by-step explanation:

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

7 = 12b^20

b = (7/12)^(1/20) = 0.9488

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Solve for "t" if:

2 = 12^t

[0.9488]^t = 1/6

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Take the log to solve for "t":

t*ln[0.9488] = ln[1/6]

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t = -1.7917 /-0.0525

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t = 34.12 minutes (this is when he will have 2mg in his blood)