A wooden boat discovered just south of the Great Pyramid in Egypt has a carbon-14 to carbon-12 ratio that is 72.5% of that found in living organisms. How old is the boat?

Carbon-14 dating is a radiometric dating method used to determine the age of organic materials by measuring the ratio of carbon-14 to carbon-12 isotopes. Living organisms continuously exchange carbon with their environment, maintaining a constant ratio of these isotopes. Upon death, the carbon-14 begins to decay at a known rate (its half-life is about 5730 years), allowing scientists to estimate the time since the organism's death based on the remaining carbon-14.

The half-life of a radioactive isotope is the time required for half of the isotope in a sample to decay into a different element or isotope. For carbon-14, this period is approximately 5730 years. Understanding half-life is crucial for calculating the age of an object based on the remaining amount of carbon-14, as it provides a consistent measure of decay over time.

Radioactive decay refers to the process by which unstable atomic nuclei lose energy by emitting radiation. The ratio of carbon-14 to carbon-12 in a sample can indicate how long it has been since the organism died. In this case, the boat's carbon-14 to carbon-12 ratio being 72.5% of that in living organisms suggests a specific amount of time has passed, which can be calculated using the known decay rate of carbon-14.