While exploring a coal mine, scientists found plant fossils which had been preserved by an earthquake in the ceiling of the mine. samples taken from one of the fossils had carbon‑14 activities of 40.0 counts/min.40.0 counts/min. a reference sample of the same size from a plant alive today has a carbon-14 activity of 160.0 counts/min.160.0 counts/min. if carbon‑14 has a half-life of 5730 years, what is the age of the plant fossil in years?

11460 years old.

t = \frac{ln(A0/A)}{ln(2)}*thalf-life = \frac{ln(160/40)}{ln(2)}*5730 = 11460

Explanation:

    Carbon 14 is formed from the collision between cosmic rays and nitrogen 14, found in the earth's atmosphere.

This carbon isotope easily binds with oxygen to form carbon dioxide (14CO2), which is absorbed by plants. When a living being dies, the amount of carbon 14 decreases, which implies a radioactive decay.

    The half-life of carbon 14 (14C) is 5730 years. This means that if an organism died 5730 years ago it will have half the content of 14C.

The half-life of a radioisotope element is the time required to disintegrate half of its mass, which can occur in seconds or billions of years, depending on the intensity of the radioisotope. That is, if we have 200 g of mass of a radioactive element whose half-life is 10 years, after these 10 years the element will have 100 g of mass. Thus, the radiocarbon age of the fossil sample can be obtained by comparing the 14C / 12C specific radioactivity of this sample. In this case, the less carbon 14 found in the older sample it is.

the answer would be d : p