Final answer:
It takes two half-lives, or 11,460 years, for approximately 75% of carbon-14 to decay into carbon-12, given the half-life of carbon-14 is 5,730 years.
Step-by-step explanation:
To determine how long it takes for approximately 75% of carbon-14 (14C) to decay into carbon-12 (12C), we use the known half-life of carbon-14, which is 5,730 years. After one half-life, 50% of the original 14C remains, and after two half-lives, 25% of the original 14C remains, meaning 75% has decayed. Therefore, it takes two half-lives, which is 5,730 years × 2, for approximately 75% of carbon-14 to decay, resulting in 11,460 years.
Carbon-14 dating can accurately estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old by comparing the ratio of 14C to 12C. Correction factors derived from tree-ring dating and other methods can account for changes in this ratio over time due to factors such as fossil fuel combustion.