Concept explainers
Challenge Yourself
Living plants and animals all contain the chemical element carbon. A certain percentage of that carbon is radioactive, and scientists believe that the parentage has remained constant for thousands of years. Radioactive carbon decays, so that when an animal dies, a tiny bit of the radioactive carbon is lost each year. It is known that the amount of radioactive carbon that remains in a fossil at the end of a year is approximately 0.99988 of the amount that was present at the beginning. Thus, the following dynamical system describes radioactive carbon
decay in a fossil:
This system behaves exactly like the compound interest situation (except the amount or radioactive carbon is decreasing), so it is easy to see that after k years, the amount of radioactive carbon in the fossil will be
Carbon dating. A fossilized bone is found that contains 90% of the original radioactive carbon that was present. To the nearest 100 years, how old is the bone?
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Mathematics All Around (6th Edition)
- Use 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_forwardRachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?arrow_forwardExplain why the values of an increasing exponentialfunction will eventually overtake the valuesof anincreasing linear function.arrow_forward
- 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_forwardUse a calculator to help solve each problem. Drug absorption in nonsmokers For a nonsmoker, the biological half-life of theophylline is 8 hours. Find the amount of the drug retained in nonsmokers system 12 hours after taking one-unit dose.arrow_forwardHeart Disease In a certain country, the number of deaths due to heart disease decreased from 235 in one year to 221 in the next year. What percentage decrease in deaths due to heart disease does this represent?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage