A mammoth skeleton has a carbon-14 content of 12.50 of that found in living organisms

True/False

Correct Question:

A mammoth skeleton has a carbon-14 content of 12.50% of that found in living organisms. When did the mammoth live?

Answer:

17,190 years ago.

Explanation:

The carbon-14 is a carbon isotope that has a half-life of 5730 years. It means that the mass of carbon-14 decreases by half every 5730 years. If we call the initial mass as M and the final mas as m:

m = M/2ⁿ

Where n is the amount of half-live that had past. Thus, in this case, the mass of the skeleton is the final mass, and the mass founded in the living organisms the initial mass, so:

m = 0.1250M, and

0.1250M = M/2ⁿ

2ⁿ = M/0.1250M

2ⁿ = 1/0.1250

2ⁿ = 8

2ⁿ = 2³

n = 3

So it had past 3 half-live or

3*5730 = 17,190 years.

So the mammoth lived 17,190 years ago.