SOLUTION: You go to the doctor and he gives you 12 milligrams of radioactive dye which decays exponentially. After 12 minutes, 4.75 milligrams of dye remain in your system. To leave the doct

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Question 978543: You go to the doctor and he gives you 12 milligrams of radioactive dye which decays exponentially. After 12 minutes, 4.75 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 you have to remain at the doctor's office, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
y=p%2Ae%5E%28-kt%29

ln%28y%29=ln%28p%29-kt
ln%28y%29-ln%28p%29=-kt
kt=ln%28p%29-ln%28y%29
k=%28ln%28p%29-ln%28y%29%29%2Ft
-
k=%28ln%284.75%29-ln%2812%29%29%2F12
k=-0.07723
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y=p%2Ae%5E%28-0.07723%2At%29

What you want to answer the question is this:
highlight%28t=%28ln%28p%29-ln%28y%29%29%2Fk%29, and let y=2, k already been found, and p given.