Question 950617: You go to the doctor and he gives you 10 milligrams of radioactive dye. After 12 minutes, 6.5 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 nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! You go to the doctor and he gives you 10 milligrams of radioactive dye. After 12 minutes, 6.5 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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apply the exponential function:
A = Pe^(rt)
from:"You go to the doctor and he gives you 10 milligrams of radioactive dye. After 12 minutes, 6.5 milligrams of dye remain in your system."
we can find r:
6.5 = 10e^(r*12)
6.5/10 = e^(12r)
.65 = e^(12r)
ln(.65) = 12r
ln(.65)/12 = r
.
Our equation is now:
A = 10e^(t*ln(.65)/12)
.
now we can answer:
how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived?
2 = 10e^(t*ln(.65)/12)
.2 = e^(t*ln(.65)/12)
ln(.2) = t*ln(.65)/12
12ln(.2) = t*ln(.65)
12ln(.2)/ln(.65) = t
44.83 = t
rounding:
45 minutes = t (answer)
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