Problem 76 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because carbon-14 decays exponentially, carbon dating can determine the ages of ancient fossils.

Step-by-Step Solution

Answer

The statement makes sense. Carbon-dating is possible due to Carbon-14's exponential decay rate.

Step 1: Understanding Carbon-14 and Carbon Dating

Carbon-14 atom is unstable, thus it gradually decays over time. It decays into nitrogen-14 through a process called beta decay. Any living organism is constantly exchanging carbon-14 with its environment, so the mixture of carbon-12 and carbon-14 within it will be the same as the mixture in the atmosphere. After death, the exchange of carbon stops and the carbon-14 slowly decays, therefore, using this knowledge, we can measure the amount of carbon-14 left in any dead thing, compare it to the regular level of carbon-14 in a living thing and thus calculate approximate time of the organism's death. This is what's called 'Carbon Dating'.

Step 2: Assessment of the Statement

Given our understanding about Carbon-14 and Carbon Dating, the statement 'Because carbon-14 decays exponentially, carbon dating can determine the ages of ancient fossils.' indeed makes sense. Radioactive decay and particularly decay of Carbon-14 is an exponential process, this property mixed with the knowledge of life cycle of carbon in any living being lets us determine the age of ancient fossils and artifacts leveraging Carbon-14 dating.

Step 3: Explanation of the Reasoning

The reasoning behind the statement is twofold. First, the fact that Carbon-14 decays exponentially, following a predictable decay curve makes it feasible to calculate the time since death of the organism. Second, Carbon dating relies on the principle that while an organism is alive, it will continue to take in carbon-14, but once it dies, it stops absorbing carbon-14. As the carbon-14 decays, we can measure the remaining ratio of carbon-14 to carbon-12 and estimate when the organism died, hence determining the ages of fossils.