Question

You go to the doctor and he gives you 13 milligrams of radioactive dye. After 20 minutes, 4.5 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

you know that the amount remaining after t minutes is

f(t) = 13 e^(-kt)
Now you know that
13 e^(-20k) = 4.5
k = 0.053, so

f(t) = 13 e^(-0.053t)

Now you want the alarm to sound when p(t) = 2. So, just find t where

13 e^(-0.053t) = 2.0