The iceman known as Otzi was discovered on a mountain on the Austrian-Italian border. Samples of his hair and bones had carbon-14 activity that was about 12.5% of that present in new hair or bone. How long ago did Otzi live if the half-life for C-14 is 5730 years

1432.5 years

Explanation:

The rate of decay of a radioactive isotope is the characteristics of the isotope and it is usually expressed in terms of its half-life.

The half-life of a radioactive element is the time taken for half of the total number of atoms in a given sample of the element to decay or the time taken for the intensity of radiation to fall to half of its original value.

From the given question.

Since the same of his bones had a carbon-14 activity that was about 12.5% of that present in new hair or bone.

Thus; the time taken to reduce the amount of the sample to one-quarter of its amount (12.5%) = the half life for C-14 (5730 years)

The time taken for how long Otzi live = 5730/4 = 1432.5 years