An artifact was found and tested for its carbon-14 content. If 84% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.
.84 = 1(.5)^(t/5730)
ln .84 = ln (.5^(t/5730) )
ln .84 = (t/5730) ln .5
t/5730 = ln .84/ln .5 = .251538767
t = 1441.317
to the nearest 100 years it would be 1400 years
where did you get ,5 from?
To determine the probable age of the artifact based on its carbon-14 content, we can use the concept of half-life.
The half-life of carbon-14 is 5,730 years, which means that after each 5,730 years, the amount of carbon-14 in a sample will decrease by half.
Given that 84% of the original carbon-14 content is still present, this means that 16% (100% - 84%) has decayed.
To calculate the number of half-lives that have passed, we can use the formula:
Number of Half-Lives = (ln(Percentage Remaining) / ln(1/2))
Using this formula, we can calculate the number of half-lives:
Number of Half-Lives = (ln(16%) / ln(1/2))
Now let's calculate this value using a calculator:
Number of Half-Lives ≈ (ln(0.16) / ln(0.5))
Number of Half-Lives ≈ (-1.832 / -0.693)
Number of Half-Lives ≈ 2.64
Since we know that each half-life is equal to 5,730 years, we can multiply this by the number of half-lives to determine the probable age of the artifact:
Probable Age = Number of Half-Lives * Half-Life
Probable Age ≈ 2.64 * 5,730
Probable Age ≈ 15,109.2 years
To the nearest 100 years, the probable age of the artifact is approximately 15,100 years.