Concept explainers
In Exercises 6—10, we consider the phenomenon of radioactive decay which, from experimentation, we know behaves according to the law:
The rate at which a quantity of a radioactive isotope decays is proportional to the amount of the isotope present. The proportionality constant depends only on which radioactive isotope is used.
10. The radioactive isotope I-131 is used in the treatment of hyperthyroidism. When administered to a patient, I-131 accumulates in the thyroid gland, where it decays and kills part of that gland.
(a) Suppose that it takes 72 hours to ship I-131 from the producer to the hospital.
What percentage of the original amount shipped actually arrives at the hospital? (See Exercise 7.)
(b) If the I- 131 is stored at the hospital for an additional 48 hours before it is used, how much of the original amount shipped from the producer is left when it is used?
(c) How long will it take for the I-131 to decay completely so that the remnants can be thrown away without special precautions?
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Chapter 1 Solutions
Differential Equations
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