An artifact was found with 63.8% of Carbon 14, how old is the mummy, assuming the half-life of Carbon 14 is 5730 years.
.638 = 1(1/2)^(t/5730)
log .638 = (t/5730)log .5
t/5730 = log .638/log .5 = .64837...
t = appr 3715 years
A scientist determined that the bones from a mastodon had lost 79.579.5% of their carbon-14. How old were the bones at the time they were discovered?
To determine the age of the mummy, we can use the concept of carbon dating, which relies on the decay of carbon-14. Carbon-14 is an isotope that is present in small amounts in the atmosphere and is absorbed by living organisms during the process of photosynthesis.
The half-life of carbon-14 is the time it takes for half of the carbon-14 in a sample to decay. In the case of carbon-14, its half-life is approximately 5730 years.
Given that the artifact contains 63.8% of the original carbon-14, we can determine the number of half-lives that have passed. We can then multiply this by the length of one half-life to calculate the approximate age of the mummy.
Let's break down the process step by step:
Step 1: Calculate the fraction of remaining carbon-14:
Fraction of remaining carbon-14 = 63.8% / 100% = 0.638
Step 2: Calculate the number of half-lives:
Number of half-lives = logarithm(base 0.5) of (fraction of remaining carbon-14)
To find the logarithm, we can use the logarithm function on a scientific calculator or an online calculator. Evaluating this:
Number of half-lives ≈ logarithm(base 0.5) of (0.638) ≈ 0.502
Step 3: Calculate the age of the mummy:
Age of the mummy ≈ Number of half-lives * Half-life of carbon-14
Age of the mummy ≈ 0.502 * 5730 years
Therefore, the approximate age of the mummy is approximately 2873 years.