How old is a sample that contains 25% of its original K-40?

When we talk about the age of a sample that contains 25% of its original K-40, we are actually referring to the concept of radioactive decay. Radioactive decay is a natural process that occurs in certain elements, such as Potassium-40 (K-40), where unstable nuclei transform into more stable nuclei by emitting radiation.

In the case of K-40, it has a half-life of 1.25 billion years, which means that after each half-life period, the amount of K-40 in the sample is reduced by half. So, if a sample contains only 25% of its original K-40, it has undergone two half-lives, as 25% is equivalent to half of half (1/2 * 1/2 = 1/4).

By calculating the time period corresponding to two half-lives of K-40, which is 1.25 billion years per half-life, we find that the sample with 25% K-40 is around 2.5 billion years old. This is because 2 * 1.25 billion years equals 2.5 billion years, making the correct answer for the sample's age option c) 2.5 billion years.