Question

How old is a piece of cotton cloth if the half-life of carbon-14 is 5,730 years, and the carbon-14 composition of the cloth is 22 percent that of living plants?

A) 1.21 × 10-4 years-1

B) 1.21 × 10-4 years

C) 1,813 years

D) 12,517 years

Answer 1

The cotton cloth is approximately 1,813 years old.

Step-by-step explanation:

To determine the age of the cotton cloth, we can use the concept of carbon dating. Carbon-14 is an isotope that can be used to determine the age of organic artifacts. The half-life of carbon-14 is 5,730 years, which means that after 5,730 years, half of the carbon-14 in a sample decays. In this case, the carbon-14 composition of the cloth is 22 percent that of living plants. Since the cloth has a lower carbon-14 composition than living plants, it must be older than the living plants.

To calculate the age of the cloth, we can use the formula: age = (t 1/2 / ln 2) x ln (initial carbon-14 composition / current carbon-14 composition).

Plugging in the values, we get: age = (5730 / ln 2) x ln (1 / 0.22) = 1,813 years.

Answer 2

The age of the cotton cloth can be determined using radiocarbon dating. In this case, it is approximately 12,517 years old.

Step-by-step explanation:

The age of a piece of cotton cloth can be determined using radiocarbon dating. The half-life of carbon-14 is 5,730 years. The carbon-14 composition of the cloth is 22 percent that of living plants. By comparing the carbon-14 disintegration rate of the cloth to the current disintegration rate, we can estimate the age of the cloth. In this case, the cloth is approximately 12,517 years old, so the correct answer is D) 12,517 years.