Question

You go to the doctor and he gives you 12 milligrams of radioactive dye. After 12 minutes, 7.5 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?

Answer 1

initial amount = 12 milligram

after 12 minutes the amount is 7.5 milligram

let the function of decay can be given as where a is the decay constant & t is in minutes

thus

=> a = 0.96159

thus decay function is

thus to pass the test

=>  

thus it will take atleast 45.7465 minutes approximately 46 minutes to pass the test