a student in Greece discovers a poetry bowl that contains 28% of its original amount of c-14
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To find out how old the poetry bowl is, we can use the concept of carbon dating. Carbon dating is a method that scientists use to determine the age of organic materials that contain carbon-14 (C-14), which is a radioactive isotope.
The first step is to understand the concept of C-14 decay. C-14 is an isotope that is naturally present in the atmosphere, and it is absorbed by plants during photosynthesis. When an organism dies, it no longer takes in new carbon, and the C-14 in its body starts to decay at a known rate. This decay follows an exponential decrease model.
Now, let's apply this to the student's discovery of the poetry bowl. If the poetry bowl contains 28% of its original amount of C-14, it means that the remaining 72% has decayed over time. We can assume that the original amount of C-14 was 100%.
To determine the age of the poetry bowl, we need to find out how many half-lives have passed. The half-life of C-14 is approximately 5730 years, meaning that it takes 5730 years for half of the C-14 in a sample to decay.
To find the number of half-lives, we can use the formula:
Number of half-lives = (ln(remaining C-14) / ln(0.5))
ln represents the natural logarithm.
Let's plug in the values:
ln(0.72) / ln(0.5) = 0.313 / (-0.693) = -0.451
Since we get a negative value, take the absolute value:
| -0.451 | = 0.451
Therefore, the number of half-lives is approximately 0.451.
To find the age of the poetry bowl, we can multiply the number of half-lives by the half-life of C-14:
Age = 0.451 x 5730 = 2585.73 years
Based on these calculations, we can estimate that the poetry bowl is approximately 2585.73 years old.