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 in this case has 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 large compared to the biological half-lives.

This problem looks pretty bad at first, but if you procede carefully, you will find it less difficult than it appears.

Consider the last sentence. If Tp >> Tb, then we know

This implies that p is so small, we can ignore it. Consequently, the effective and biological decay constants will be equal for any one goat.

The time is:
A. 0.53 day
B. 1.46 day
C. 19 day
D. 27 day
E. 146 day


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