Skeletal remains had lost 70% of the C-14 they originally contained. Determine the approximate age of the bones. (Assume the half life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
To determine the approximate age of the bones, we can use the concept of half-life and the percentage of C-14 remaining.
1. Start by understanding the concept of half-life: The half-life of carbon-14 (C-14) is the time it takes for half of the C-14 atoms in a sample to decay. In this case, the given half-life of C-14 is 5730 years.
2. Since the skeletal remains have lost 70% of the C-14 they originally contained, this means that only 30% (100% - 70%) of the C-14 remains.
3. To find out how many half-lives have passed, we can use the following formula:
Number of half-lives = (ln(percentage remaining) / ln(0.5))
Let's plug in the values:
Number of half-lives = (ln(30%) / ln(0.5))
4. Using a calculator, calculate the natural logarithm (ln) of 30% and divide it by the natural logarithm of 0.5.
5. Once you have the result, divide it by the given half-life of carbon-14 (5730 years). This will give you the number of half-lives that have passed.
6. Finally, multiply the number of half-lives by the half-life of carbon-14 (5730 years) to find the approximate age of the bones.
For example, if the calculated number of half-lives is 3.2, the approximate age of the bones would be 5730 years × 3.2 = 18336 years. Round your final answer to the nearest whole number.
the fraction remaining after t years is
(1/2)^(t/5730)
So, you want
(1/2)^(t/5730) = .7
t/5730 = log(.7)/log(.5)
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