   Chapter 6.2, Problem 32E

Chapter
Section
Textbook Problem

Radioactive Decay In Exercises 29-36, complete the table for the radioactive isotope.Isotope Half-life (in years) Initial Quantity Amount After 1000 Years Amount After 10,000 Years 14 C 5715 _____ _____ 3   g

To determine

To calculate: The initial amount of the radioactive isotope 14C and its total amount after 1000 years.

Explanation

Given:

Half-life of the radioactive isotope 14C as 5715 and its amount after 10,000 years as 3g

Formula used:

We can use growth and decay model y=Cekt.

Logarithmic property:

ln(ex)=x

Also,

eln(x)=x

Calculation:

Let us consider the given expression:

y=Cekt …… (1)

Let the initial amount be C.

t=10000 for the amount after 10,000 years and also given that y=3.

By putting t=10000 and y=3 in equation (1), we get:

y=Cekt3=Cek×10000C=3e10000k

For half-life, t=5715 and y=12C.

By putting t=5715 and y=12C in equation (1), we get:

y=Cekt12C=Cek×571512=e5715kln(12)=ln(e5715k)

By simplifying further,

5715k=ln(12)5715k=0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Differentiate the function. y=3ex+4x3

Single Variable Calculus: Early Transcendentals, Volume I

In the problem 1-4, solve the equations 3x14x9=57

Mathematical Applications for the Management, Life, and Social Sciences

Find f(x) if f(x) = 10x2 + cos x. a) 20x sin x + C b) 20x cos x + C c) 103x3cosx+C d) 103x3+sinx+C

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