An artifact was found and tested for its carbon-14 content. If 74% of the orginal carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half life of 5730 years).

(1/2)^(t/5730) = .74

t = 5730 * log(.74)/log(0.5)

To determine the probable age of the artifact, we need to use the concept of half-life and the percentage of the original carbon-14 that remains.

The half-life of carbon-14 is 5730 years, which means that after every 5730 years, the amount of carbon-14 in a sample decreases by half.

Let's assume that the original amount of carbon-14 in the artifact was 100%. If 74% of the original carbon-14 content remains, this means that 26% has decayed over time.

Now, we know that after every half-life, the remaining carbon-14 is halved. Therefore, we can calculate how many half-lives it took for the carbon-14 to decay from 100% to 26%.

26% = 100% * (1/2)^(n), where 'n' is the number of half-lives.

To solve this equation, we can take the logarithm of both sides. Using the logarithm base 0.5 (since (1/2) = 0.5), we can rewrite the equation as:

log base 0.5 (26%) = n

By evaluating the left side of the equation, we can find the value of 'n'.

n ≈ 0.6772

Since 'n' represents the number of half-lives that have passed, we need to multiply it by the half-life of carbon-14 (5730 years) to find the total amount of time that has passed:

Total time = n * half-life = 5730 years * 0.6772 ≈ 3889.968 years

Rounding this value to the nearest hundred years, the probable age of the artifact is approximately 3900 years.