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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider
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In 23–27, assume that the rate of decay of a radioactive

Chapter 3, Problem 24E

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QUESTION:

Problem 24E

Problem

In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate.

If initially there are 300 g of a radioactive substance and after 5 yr there are 200 g remaining, how much time must elapse before only 10 g remain?

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QUESTION:

Problem 24E

Problem

In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate.

If initially there are 300 g of a radioactive substance and after 5 yr there are 200 g remaining, how much time must elapse before only 10 g remain?

ANSWER:

Solution:-

Step1

Given that

We have to find how much time must elapse before only 10 g remain,if initially there are 300 g of a radioactive substance and after 5 yr there are 200 g remaining.

Step2

Suppose  is the initial radioactive substance .

So,

Suppose M(t) is the remaining substance after t times.

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