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

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Chapter 4.4, Problem 82E
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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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Carbon Dating In Exercises 79–82, you are given the ratio of carbon isotopes to carbon atoms in a fossil. Use the information to estimate the age of the fossil. In living organic material, the ratio of radioactive carbon isotopes to the total number of carbon atoms is about 1 to 1012. (See Example 3 in Section 4.1.) When organic material dies, its radioactive carbon isotopes begin to decay, with a half-life of about 5715 years. So, the ratio R of carbon isotopes to carbon-14 atoms is modeled by R = 10 − 12 ( 1 2 ) t / 5715 , where t is the time (in years) and t = 0 represents the time when the organic material died.

R = 0.13 × 10 − 12

To determine

To calculate: The age of the fossil when the ratio of carbon isotopes to carbon atoms in a fossil is R=0.13×10−12 and the formula to calculate the ratio R is given by R=10−12(12)t5715, where t is the time in years and t=0 is the time when the organic material died.

Explanation

Given Information:

The ratio of carbon isotopes to carbon atoms in a fossil is R=0.13×10−12 and the formula to calculate the ratio R is given by R=10−12(12)t5715, where t is the time in years and t=0 is the time when the organic material died.

Formula used:

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

Calculation:

Consider the provided information that the ratio of carbon isotopes to carbon atoms in a fossil is R=0.13×10−12 and the formula to calculate the ratio R is given by R=10−12(12)t5715, where t is the time in years and t=0 is the time when the organic material died.

Consider the equation, R=10−12(12)t5715

Here, R=0.13×10−12

Calculate the age of fossil by substituting the value of R in the equation as,

0.13×10−12=10−12(12)t5715

Divide both sides by 10−12 as,

0.13×10−1210−12=10−12(12)t571510−120

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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
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In Exercises 116, determine whether the argument is valid. pqqrpr

Finite Mathematics for the Managerial, Life, and Social Sciences

Given: ABCPRC,mA=67,PC=5,CR=12,PR=13,AB=26 Find: a mB b mRPC c AC d CB

Elementary Geometry for College Students

Slope Field In Exercises 55 and 56, a differential equation, a point, and a slope field are given, (a) Sketch t...

Calculus (MindTap Course List)

Converting Rectangular CoordinatesIn Exercises 61 and 62, convert the point from rectangular coordinates to (a)...

Multivariable Calculus

True or False: The graph at the right is the graph of an even function.

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

Area In Exercises 115 and 116, find the area of the given region. y=616+x2

Calculus

The point plotted at the right has coordinates: (2, 5, 4) (5, 2, 4) (4, 2, 5) (2, 4, 5)

Study Guide for Stewart's Multivariable Calculus, 8th

Use matrix inversion to solve each system of equations. Note that several systems have the same coefficient mat...

College Algebra (MindTap Course List)

Referring to the previous exercise, use the result of Part (a) along with the fact that a carton contains 12 eg...

Introduction To Statistics And Data Analysis

Show the box plot for the data in exercise 46.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe how time, event, or individual sampling is done during behavioral observation, and explain why samplin...

Research Methods for the Behavioral Sciences (MindTap Course List)

List the five sections typically found in a research article, and describe briefly what each should contain.

Research Methods for the Behavioral Sciences (MindTap Course List)

Registered nurses in 2007 made an average hourly wage of 30.04. In 2011, their hourly wage had risen to 33.23. ...

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

a. Given: EB=5.150. Determine AE . b. Given: AE=4.200. Determine AB.

Mathematics For Machine Technology

In Exercises 4150, determine how many cards, in an ordinary deck of fifty-two, fit the description. If you are ...

Mathematics: A Practical Odyssey

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