Two goats at Port Hopeless, Ontario accidentally get into a field containing rad

Question

Two goats at Port Hopeless, Ontario accidentally get into a field containing radioactive grass. The goat "Aristophanes" eats twice as much grass as the goat "Demetrius". However Aristophanes' metabolism is 1.5 times faster than that of Demetrius and the ingested isotope has in this case a biological decay constant which is directly proportional to metabolism. If the biological decay constant is 0.10 day-1 in Demetrius, how long will it be until the two goats contain the same concentration of isotope? Assume that the physical half life is very long compared to the biological half lives.

Ans: 14 days

Explanation / Answer

Let y be the amount of radioactive material in the goat, and y0 be the initial amount. Demetrius y' = -.10y y = y0*e^(-.10t) Aristophanes y' = -.15y y = 2*y0*e^(-.15t) Set the amount in each goat equal: y0*e^(-.10t) = 2*y0*e^(-.15t) Divide each side by y0: e^(-.10t) = 2*e^(-.15t) Take the ln of both sides: -.10t = ln(2) -.15t .05t = ln(2) t = ln(2)/.05 t = 13.86 which is about 14

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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