SOLUTION: You go to the doctor and he gives you 15 milligrams of radioactive dye. After 12 minutes, 4.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass

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Question 851519: You go to the doctor and he gives you 15 milligrams of radioactive dye. 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 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 josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential Decay, p=15e%5E%28-kt%29.
Find k.
ln%28p%29=ln%2815%29%2B%28-kt%29ln%28e%29
-kt=ln%28p%29-ln%2815%29
kt=ln%2815%29-ln%28p%29---------remember this step for later.
k=%281%2Ft%29%28ln%2815%2Fp%29%29
Value for k.
k=%281%2F12%29%28ln%2815%2F4.75%29%29
highlight_green%28k=0.0958%29
-
More specific model is p=15e%5E%28-0.0958t%29 and you want to know t when p=2.
Using earlier referenced step,
highlight%28t=%281%2F0.0958%29%28ln%2815%2F2%29%29%29
21 minutes.