Half-life describes the amount of time for a radioactive substance to decay to one-half of the original substance’s weight. So, if we had 100g of C-14, after 5,730 years, only 50g remain; after another 5,730 years, only 25g would remain, and so on.
In this problem, we are meant to assume that the original amount of C-14 was 64g, and that, through decay, it forms N-14. We can figure out how many half lives have passed by figuring out how much 4 is out of 64 by dividing 64 by two repeatedly. Each time, count a half life.
64 - 32 (1 HL) - 16 (2 HL) - 8 (3 HL) - 4 (4 HL)
In this problem, 4 half lives have passed. We can now multiply this by the time for one half life to find how many years have passed.
4 x 5,730 = 22,920 years
Approximately 22,920 years have passed since the drawing was created.