Final answer:
The initial sample had 4 grams of carbon-14.
Step-by-step explanation:
To determine the number of grams in the initial sample, we need to find the number of half-lives that have passed. Since carbon-14 has a half-life of 5730 years, we can calculate the number of half-lives using the formula: (t ÷ half-life). So, 1000 years ÷ 5730 years = approximately 0.174 half-lives.
Since 2 grams remain after 1000 years, and one half-life has occurred, we can assume that the original sample had twice the amount, which is 4 grams. Therefore, the initial sample had 4 grams of carbon-14.