Uranium 239 is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 1 gram of U239 was placed in a container, and the amount remaining was measured at 1-minute intervals and recorded in the table below. (Let t be the time in minutes and U the number of grams remaining.) Time in minutes Grams remaining 0 1 1 0.9710 2 0.9428 3 0.9155 4 0.8889 5 0.8632 (a) Show that these are exponential data. (Round your answer to three decimal places.) The ratios of successive terms are always  , and therefore the data are exponential.   (b) What is the percentage decay rate each minute? (Round your answer to one decimal place.)  % What does this number mean in practical terms? This means that  % of the remaining uranium decays each minute. (c) Use functional notation to express the amount remaining after 7 minutes. U(   ) Calculate that value. (Round your answer to three decimal places.)  g (d) What is the half-life of U239? (Round your answer to three decimal places.)  min

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Topic Video
Question

Uranium 239 is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 1 gram of U239 was placed in a container, and the amount remaining was measured at 1-minute intervals and recorded in the table below. (Let t be the time in minutes and U the number of grams remaining.)

Time
in minutes
Grams
remaining
0 1
1 0.9710
2 0.9428
3 0.9155
4 0.8889
5 0.8632
(a) Show that these are exponential data. (Round your answer to three decimal places.)
The ratios of successive terms are always  , and therefore the data are exponential.
 
(b) What is the percentage decay rate each minute? (Round your answer to one decimal place.)
 %

What does this number mean in practical terms?
This means that  % of the remaining uranium decays each minute.


(c) Use functional notation to express the amount remaining after 7 minutes.
U(   )


Calculate that value. (Round your answer to three decimal places.)
 g

(d) What is the half-life of U239? (Round your answer to three decimal places.)
 min
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 9 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education