Skeletal remains had lost 81% 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.)
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Well, I must say, these bones are quite the shady characters. Losing 81% of their C-14, huh? It seems like they've been going on some pretty wild diets!
Now, let's calculate their approximate age. Since the half-life of carbon-14 is 5730 years, we can use a little math magic. If they've lost 81% of their C-14, that means they still have 19% left.
So, the equation looks something like this:
Age of bones = (5730 years) / (0.19)
Calculating this, we get approximately 30158 years.
So there you have it, these bones are approximately 30158 years old. That's ancient! Hope that answers your question, and remember, it's no joke when it comes to carbon dating!
To determine the approximate age of the bones, we can use the concept of half-life. The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 in a sample will have decayed.
If the skeletal remains have lost 81% of their carbon-14, it means that only 19% (100% - 81%) of the original carbon-14 remains.
Since each half-life reduces the amount of carbon-14 by half, we need to find out how many half-lives it took for the remaining carbon-14 to be 19%. This can be calculated using the formula:
Number of half-lives = (ln(Percentage remaining) / ln(0.5))
Number of half-lives = (ln(19%) / ln(0.5))
Using a calculator, we find that the number of half-lives is approximately 3.513.
Since each half-life is 5730 years, we can multiply the number of half-lives by the half-life value to determine the approximate age of the bones:
Approximate age of bones = Number of half-lives * Half-life
Approximate age of bones = 3.513 * 5730
Approximate age of bones = 20152 years.
Therefore, rounding to the nearest whole number, the approximate age of the bones is 20152 years.
To determine the approximate age of the bones, we can use the concept of half-life of carbon-14 (C-14). The half-life of C-14 is the time it takes for half of the radioactive isotope to decay. In the case of C-14, its half-life is approximately 5730 years.
Given that the skeletal remains have lost 81% of their C-14, we can use this information to find out how many half-lives have passed.
To do this, we will use the formula: N = N0 * (1/2)^(t / T), where N is the final amount of C-14, N0 is the initial amount of C-14, t is the time that has passed, and T is the half-life of C-14.
Let's say the initial amount of C-14 in the bones was 100%. Since they have lost 81% of the C-14, we can translate this as N = 19% (the remaining C-14).
Let's substitute the values into the formula: 0.19 = 1 * (1/2)^(t / 5730)
Now we need to solve for t, the time that has passed (in years).
To isolate t, we can take the logarithm (base 1/2) of both sides of the equation:
log[1/2] (0.19) = t / 5730
Using logarithmic identities, we can rewrite the equation as:
t = log[1/2] (0.19) * 5730
Now we can calculate the approximate age of the bones using a scientific calculator or an online logarithm calculator.
The result may vary slightly depending on the calculation method, but when rounded to the nearest whole number, the approximate age of the bones is obtained.
since the half-life is 5730 years, the amount left after t years is
a = (1/2)^(t/5730)
If 81% is lost, that leaves a = 0.19, then just solve for t.
Since 1/8 < .19 < 1/4, the answer should be between 2 and 3 half-lives.