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.