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

Question

You go to the doctor and he gives you 13 milligrams of radioactive dye. After 20 minutes, 8 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.

You will spend ____ minutes at the doctor's office.

Explanation / Answer

the decay equation is y = ab^x ..................... [ I ] ,

which yields x = ln(y/a) / ln (b) ....... [ II ]

plugging into [ I ]
2 = 13* (8/13)^(t/12)

plugging into [ II ]
t/12 = ln(2/13) / ln (8/13)
t = 12*ln(2/13)/ln(8/13) = 46.26 => 46 mins

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.