Question 1080735: You go to the doctor and he gives you 11 milligrams of radioactive dye. After 24 minutes, 4.25 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 by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 4.25=11e^(-24k) ,where k is in minutes
0.3864=e^(-24k)
ln both sides, then divide by -24 and finally round
k=0.0396
now use that for 2mg
2=11*e-(kt), exponent is 0.0396t
0.182=e-(0.0396 t)
ln of both sides then divide by -0.0396, rounding at end. I would estimate the answer to be between 24 and 48 minutes, since after 24 less than half remained.
t=43.05 minutes. When one guesses a range before solving, and has a decent guess, this serves as a good check.
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