Answer:
The artifact contained 8 g of C-14 about 1,825 years ago.
Step-by-step explanation:
We can use the exponential decay formula for carbon-14 to solve this problem:
N(t) = N0 * (1/2)^(t/T)
where N(t) is the amount of carbon-14 remaining at time t, N0 is the initial amount of carbon-14, t is the time that has passed, and T is the half-life of carbon-14.
Let's first calculate how many half-lives it takes for 2 g of C-14 to decay to 1/4 of that amount, which is 0.5 g:
0.5 g = 2 g * (1/2)^(t/T)
(1/2)^(t/T) = 0.25
t/T = ln(0.25) / ln(1/2)
t/T = 2
Therefore, it takes 2 half-lives for 2 g of C-14 to decay to 0.5 g.
Now we can use the same formula to calculate how long it would take for 8 g of C-14 to decay to 2 g (which is 4 half-lives):
2 g = 8 g * (1/2)^(4T/T)
(1/2)^(4) = 2 g / 8 g
(1/2)^(4) = 0.25
4T = ln(0.25) / ln(1/2)
T = ln(0.25) / (4 * ln(1/2))
T = 1,825 years
Therefore, the artifact contained 8 g of C-14 about 1,825 years ago.