Final answer:
Using the half-life of carbon-14 and the decay formula, we can calculate the amount of carbon-14 an artifact originally contained from the current observed amount after a given number of years.
Step-by-step explanation:
To determine how much carbon-14 an artifact originally contained, we use the concept of radiometric dating, particularly focusing on carbon dating. Given the artifact contains 8.4 × 10^-9 grams of carbon-14 after 10,670 years, and knowing that the half-life of carbon-14 is 5,730 years, we can use the decay formula:
A = A0e^−0.693t/T1/2
Where A is the current amount of carbon-14, A0 is the original amount, t is the time that has passed, and T1/2 is the half-life of carbon-14. Using this formula, we can solve for A0 knowing that A is 8.4 × 10^-9 grams and t is 10,670 years, to find the original amount of carbon-14.