Concept explainers
Radioactive Decay The half-life of a radioactive substance is the time H that it takes for half of the substance to change form through radioactive decay. This number does not depend on the amount with which you start. For example, carbon-14 is known to have a half-life of
Where H is the half-life, t is the elapsed time,
a. Uranium-228 has a half-life H of 9.3 minutes. Thus, the decay function for this isotope of uranium is
where t is measured in minutes. Suppose we start with grams of uranium-228.
i. How much uranium-228 is left after 2 minutes?
ii. How long will you have to wait until there are only 3 grams left?
b. Uranium-235 is the isotope of uranium that can be used to make nuclear bombs. It has a half-life of 713 million years. Suppose we start with 5 grams of uranium-235.
i. How much uranium-235 is left after 200 million years?
ii. How long will you have to wait until there are only 3 grams left?
Trending nowThis is a popular solution!
Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Elementary Algebra For College Students (9th Edition)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
Algebra And Trigonometry (11th Edition)
Linear Algebra and Its Applications (5th Edition)
Graphical Approach To College Algebra
Intermediate Algebra (8th Edition)
- The half-life of radioactive actinium ( 227AC ) is 21.77 years. What percent of a present amount of radioactive actinium will remain after 19 years?arrow_forwardCesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?arrow_forwardTracer Dye The amount of a tracer dye injected into the blood stream decrease exponentially, with a decay constant of 3 per minute. If 6 cc are present initially, how many cubic centimeters are present after 10 minutes? Here k will be negative.arrow_forward
- Half-Life The half-life of radium-226 is approximately 1620 years. a. How much of sample weighing 4 g will remain after 100 hours? b. How much time is necessary for a sample weighing 4 g to decay to 0.1 g?arrow_forwardUse a calculator to help solve each problem. Tritium decay Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 50 grams, how much remain after 100 years?arrow_forwardAn investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?arrow_forward
- Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forwardThe half-life of a radioactive material is about 34.2 years. How much of the material is left after 20 years?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning