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?

34.12 minutes

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

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

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

answer:

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