You go to the doctor and he gives you 10 milligrams of radioactive dye which decays exponentially. After 20 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 you have to remain at the doctor's office, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.

You will spend minutes at the doctor's office.