An artifact was found and tested for its carbon-14 content. If 76% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)
.76 = 1 (1/2)^(t/5730)
log both sides:
log .76 = (t/5730) log .5
t/5730 = log .76/log .5 = .39592...
t = 2268.67 years
or
t = appr 2300 years, correct to the nearest 100 yrs.
To determine the probable age of the artifact based on its carbon-14 content, we can use the concept of half-life.
Here are the steps to find the probable age:
1. Determine the number of half-lives: The half-life of carbon-14 is 5,730 years. We need to find out how many half-lives it would take for 76% of the original carbon-14 to remain.
To calculate the number of half-lives, we can use the following formula:
Number of half-lives = log(remaining carbon-14 / initial carbon-14) / log(1/2)
Given that 76% (0.76) of the original carbon-14 is still present, the remaining carbon-14 is 0.76 times the initial carbon-14.
Number of half-lives = log(0.76) / log(1/2)
Calculating this gives us approximately 0.3219 half-lives.
2. Calculate the probable age: Now that we know the number of half-lives, we can calculate the probable age of the artifact.
Probable age = Number of half-lives × half-life of carbon-14
Probable age = 0.3219 × 5,730 years
Calculating this gives us approximately 1,845.15 years.
Therefore, the probable age of the artifact (to the nearest 100 years) is approximately 1,800 years.