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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4, Problem 28TYS
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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What percent of a present amount of radioactive plutonium (239Pu) will remain after 15,000 years? (The half-life of 239Pu is 24,100 years.)

To determine

To calculate: The remaining percent of the present amount of radioactive plutonium (239Pu) after 15,000 years if the half-life of (239Pu) is 24,100 years.

Explanation

Given Information:

The half-life of (239Pu) is 24,100 years.

Formula used:

Exponential growth and decay:

If the rate of change of a positive quantity y with respect to time is proportional to the amount of quantity present at any time t, that is dydt=ky, then y is given by the equation, y=Cekt, where C is the value of the quantity at a time t=0 and k is the constant of proportionality.

If k>0, then there is exponential growth and when k<0, then there is an exponential decay.

Calculation:

Consider the equation y=Cekt.

Here, the half-life of P239u is 24,100 years, that is, at t=24,100 the initial amount reduces to half so,

y=C2

Substitute t=24,100 and y=C2 in the equation y=Cekt.

C2=Cek×24,100C2C=e24,100k12=e24,100k

Take natural log on both the sides,

ln(e24,100k)=ln(12)24,100k⋅(lne)=ln(12

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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Defining TermsDefine each of the following for a function of two variables. (a) Relative minimum (b) Relative m...

Calculus: Early Transcendental Functions (MindTap Course List)

Using a Tangent Line In Exercises 61-64, write and evaluate the definite integral that represents the area of t...

Calculus of a Single Variable

Formulate but do not solve each of the following exercises as a linear programming problem. You will be asked t...

Finite Mathematics for the Managerial, Life, and Social Sciences

In trap. ABCD not shown, mA=x2+10, mB=x3+50, and mC=x5+50. Find all possible values of x.

Elementary Geometry for College Students

Using a Series In Exercises 69 and 70, use me given series. (a) Does the series meet the conditions or Theorem ...

Calculus

A parametrization of the cylinder in the figure is: x = u, y = v, z = v − u2, 22 ≤ u ≤ 2, 0 ≤ v ≤ 3 x = u, y = ...

Study Guide for Stewart's Multivariable Calculus, 8th

Which number is the best choice for the value of a in the following graph? a) e b) 1 c) 2 d) 3

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

CONCEPT CHECK Integration by Tables Which formula from the table of integrals would you use to find the integra...

Calculus (MindTap Course List)

Using Vectors to Determine Collinear PointsIn Exercises 17 and 18, use vectors to determine whether the points ...

Multivariable Calculus

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears....

Mathematics For Machine Technology

Three different assembly methods have been proposed for a new product. A completely randomized experimental des...

Statistics for Business & Economics, Revised (MindTap Course List)

The article The Distribution of Buying Frequency Rates (Journal of Marketing Research [1980]: 210216) reported ...

Introduction To Statistics And Data Analysis

Define primary and secondary sources and explain how each plays a role in the process of finding a research ide...

Research Methods for the Behavioral Sciences (MindTap Course List)

How does a full-text database differ from other databases?

Research Methods for the Behavioral Sciences (MindTap Course List)

Gulf Real Estate Properties Gulf Real Estate Properties, Inc., is a real estate firm located in southwest Flori...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Fill in the blanks. The point where a graph intersects the x-axis is called the _______________.

College Algebra (MindTap Course List)

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