You go to the doctor and he gives you 10 milligrams of radioactive dye. After 12 minutes, 7 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.

Question

anonymous · Answer

so my first thought is that we have two points (0,10) at zero minutes 10mg of dye, and (12,7) at 12 minutes 7mg of dye...

unklerhaukus · Answer

Yes that is a good start, you have two points of the form (time, mass), 
$(0,M_0)$ & $(t_1,M(t_1))$ The general equation for exponential decay is$$\large M(t)=M_0 e^{-\lambda t}$$ With these data points, you should be able to work out $\lambda$ the decay constant.

Next you have to determine the time that the mass is reduced to 2 mg, to do this solve the equation for t, and sub in the values

anonymous · Answer

i got it! This video also helped: https://www.youtube.com/watch?v=PEFKE_k9pDk