Final answer:
After 17,200 years, approximately 9.975 milligrams of the original 79.8 milligrams of carbon-14 would remain. This calculation uses the half-life of carbon-14 (5,730 years) to determine the amount of substance left after the elapsed time.
Step-by-step explanation:
The question involves the concept of radioactive dating, specifically the use of carbon-14 in radiocarbon dating to determine the amount of a substance that remains after a certain period of time has elapsed. The half-life of carbon-14 is 5,730 years, which means half of the carbon-14 in a sample will decay to nitrogen-14 approximately every 5,730 years. If we begin with 79.8 milligrams of carbon-14, to find how much remains after 17,200 years, we divide the time by the half-life to find how many half-lives have passed (17,200 / 5,730 ≈ 3). Since the half-life is the time for half of the material to decay, we can calculate the remaining amount by halving the original amount three times:
- First half-life: 79.8 mg / 2 = 39.9 mg remains
- Second half-life: 39.9 mg / 2 = 19.95 mg remains
- Third half-life: 19.95 mg / 2 = 9.975 mg remains
Thus, approximately 9.975 milligrams of carbon-14 would remain after 17,200 years have passed.