Final answer:
The artifact was made approximately 28,650 years ago. In the radioactive decay model, the half-life of carbon-14 is 5730 years, and since the artifact contains 80% of the carbon-14 present in living trees, we can use the decay rate formula to determine the age of the artifact.
Step-by-step explanation:
The artifact was made approximately 28,650 years ago.
In the radioactive decay model, the half-life of carbon-14 is 5730 years. Since the artifact contains 80% of the carbon-14 that is present in living trees, it means that 20% of the original carbon-14 has decayed. To determine the time it takes for 20% of carbon-14 to decay, we can use the formula:
r = 1 - (1/2)t/h
Where r is the decay rate, t is the time in years, and h is the half-life.
Substituting the given values, we have:
r = 0.20, h = 5730 years
By solving for t, we find:
t = h * log2(1 - r)
Rounding the decay rate to 6 decimal places as instructed, we have r = 0.200000.
Plugging in the values, we have:
t = 5730 * log2(0.800000)
After solving, we find that t is approximately 28,650 years.