Explanation Given information: The provided information is: If a breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount present at any time. After 10 years, 0.03 % of the radioactivity has dissipated. Suppose that initially there is 100 pounds of this substance. Formula used: Half-life can be defined as: d y d t = − k t and after several it gives y = A e − k t . When a differential equation can be equivalently expressed in the form: g ( y ) d y = f ( x ) d x This is known as variable separable. Calculation: Consider the provided information: If a breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount present at any time. After 10 years, 0.03 % of the radioactivity has dissipated. Suppose that initially there is 100 pounds of this substance. Half-life can be defined as: d y d t = − k t and after several it gives y = A e − k t . When a differential equation can be equivalently expressed in the form: g ( y ) d y = f ( x ) d x This is known as variable separable. It is provided that if t = 0 than y = 100 and thus the value of A = 100

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Differential Equations

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Chapter 12.5, Problem 47E

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To calculate: The half-life if a breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount present at any time. After 10 years, 0.03% of the radioactivity has dissipated. Suppose that initially there is 100 pounds of this substance.

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Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The half-life if a breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount present at any time. After 10 years, 0.03 % of the radioactivity has dissipated. Suppose that initially there is 100 pounds of this substance.

Solution Summary: The author calculates the half-life if a breeder reactor converts uranium into an isotope of plutonium-239.

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To calculate: The half-life if a breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to the amount present at any time. After 10 years, 0.03% of the radioactivity has dissipated. Suppose that initially there is 100 pounds of this substance.

Chapter 12 Solutions