Carbon-14 has a half-life of 5730 years. in a plant fossil, you find that the 14c has decayed to 1/8.00 of the original amount. how long ago was this plant alive? .

Note that 8.00 = (2.00)^3, that implies that a decay to 1/8.00 means that the Carbon-14 has passed 3 half-life. (1 to decay to 1/2, other to decay to 1/4, and other to decay to 1/8). And, three half-life is 3 * 5730 years = 17,920 years. So, the answer is that the plant was alive 17,920 years.