You go to the doctor and he gives you 12 milligrams of radioactive dye.

Question

You go to the doctor and he gives you 12 milligrams of radioactive dye. After 16 minutes, 7.25 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? Give your answer to the nearest minute.

Answer 1

P=12 mg initially in your system

when will you have 2 mg in your system?

7.25 mg after 16 minutes

7.25 = 12e^16r where r=rate of change per minute

7.25/12 = e^16r

16r = ln(7.25/12)

r = (ln(7.25/12))/16 =about -.0315

2 = 12e^-.0315t

e^-.0315t = 2/12 =1/6

-.0315t = ln(1/6)

t = (ln(1/6))/-.0315 = about 56.88 minutes to reach 2 mg left in your system

= about 57 minutes before the alarm stops going off