SOLUTION: You go to the doctor and he gives you 13 milligrams of radioactive dye. After 24 minutes, 6.5 milligrams of dye remain in your system. To leave the doctor's office, you must pass t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: You go to the doctor and he gives you 13 milligrams of radioactive dye. After 24 minutes, 6.5 milligrams of dye remain in your system. To leave the doctor's office, you must pass t      Log On


   

Question 1158943: You go to the doctor and he gives you 13 milligrams of radioactive dye. After 24 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 josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
6.5=13e%5E%28k%2A24%29, using continuous exponential decay model
13e%5E%2824k%29=6.5
e%5E%2824k%29=6.5%2F13
ln%28e%5E%2824k%29%29=ln%286.5%2F13%29
24k=ln%286.5%2F13%29=ln%281%2F2%29
k=ln%281%2F2%29%2F24
k=-0.02888

If 2 milligrams, how much time, x?
ln%28e%5E%28-0.02888x%29%29=ln%282%2F13%29
-0.02888x=ln%282%2F13%29
x=-ln%282%2F13%29%2F0.02888
highlight%28x=65%29minutes