12. Dinosaur fossils are too old to be reliably dated using carbon-14. (See Exercise 11.) Suppose we had a 68-million- year-old dinosaur fossil. What fraction of the living dino- saur's ¹C would be remaining today? Suppose the minimum detectable amount is 0.1%. What is the maximum age of a fossil that we could date using ¹4C?
12. Dinosaur fossils are too old to be reliably dated using carbon-14. (See Exercise 11.) Suppose we had a 68-million- year-old dinosaur fossil. What fraction of the living dino- saur's ¹C would be remaining today? Suppose the minimum detectable amount is 0.1%. What is the maximum age of a fossil that we could date using ¹4C?
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Exercise 12: Understanding Carbon-14 Dating in Paleontology**
Dinosaur fossils are too old to be reliably dated using carbon-14. (Refer to Exercise 11 for more context.) Given a 68-million-year-old dinosaur fossil, consider the following questions:
1. **Current Carbon-14 Fraction in Fossils**: What fraction of the living dinosaur's carbon-14 would still be present today?
2. **Detection Limit**: Assume the minimum detectable amount of carbon-14 is 0.1%.
3. **Maximum Dating Age with Carbon-14**: What is the maximum age of a fossil that carbon-14 dating could accurately evaluate?
Transcribed Image Text:### Understanding Radiocarbon Dating
**Radiocarbon Dating Explained:**
Scientists have developed a method called radiocarbon dating to determine the age of ancient objects. This approach leverages the transformation process occurring in the Earth's upper atmosphere, where cosmic rays convert nitrogen into a radioactive carbon isotope, known as carbon-14 (^14C). This isotope has a half-life of approximately 5730 years.
**Absorption by Living Organisms:**
Living plants absorb carbon dioxide, which includes carbon-14, through the atmosphere. Animals then incorporate this radioactive carbon into their systems by consuming plants or other animals.
**Decay After Death:**
Once an organism dies, it ceases the intake of carbon, leading to a gradual decrease in the ^14C content due to radioactive decay. Consequently, the level of radioactivity decreases exponentially over time.
**Application to Historical Analysis:**
Researchers discovered a parchment fragment exhibiting around 74% of the carbon-14 radioactivity level found in living plant material today. This decay in radioactivity allows scientists to estimate the age of historical artifacts like this parchment.
By applying the principles of radiocarbon dating, the age of ancient objects and historical records can be effectively estimated, enriching our understanding of historical timelines.
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