Final answer:
The half-life of the substance is 5,000 years.
Step-by-step explanation:
The half-life of a substance can be determined by calculating the time it takes for half of the original sample to decay. In this case, the substance decayed from 250 grams to 7.812 grams over a period of 25,000 years. To find the half-life, we divide the total time by the number of times the substance was halved. In this case, the substance was halved approximately 5 times (250 --> 125 --> 62.5 --> 31.25 --> 15.625 --> 7.812), so the half-life is 25,000 years divided by 5, which is 5,000 years.