   Chapter 12.5, Problem 47E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Half-life 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 (that is, 0.9997 of the initial amount remains). Suppose that initially there is 100 pounds of this substance. Find the half-life.

To determine

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.

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:

dydt=kt and after several it gives y=Aekt.

When a differential equation can be equivalently expressed in the form:

g(y)dy=f(x)dx

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:

dydt=kt and after several it gives y=Aekt.

When a differential equation can be equivalently expressed in the form:

g(y)dy=f(x)dx

This is known as variable separable.

It is provided that if t=0 than y=100 and thus the value of A=100

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