Carbon-14 has a half-life of approximately 5,730 years. How many half-lives have occurred in a sample that contains 50 percent of the original amount of the parent isotope?

exactly one.

The half-life is the time it takes to reduce to one-half (50%) of the original value.

please answer my question

To determine the number of half-lives that have occurred in a sample containing 50 percent of the original amount of carbon-14, we can use the formula:

Number of half-lives = (log(R) / log(1/2))

Where "R" is the ratio of the remaining amount to the original amount, which is 50 percent or 0.5 in this case.

Let's calculate the number of half-lives:

Number of half-lives = (log(0.5) / log(1/2))

To solve this equation, we need to use logarithmic properties. The logarithm of 0.5 to the base 2 is approximately -1.

Number of half-lives = (-1 / log(1/2))

The logarithm of 1/2 to the base 10 is approximately -0.301.

Number of half-lives = (-1 / -0.301) = 3.32

The result indicates that approximately 3.32 half-lives have occurred in the sample. Since it is not possible to have a fraction of a half-life, we can round this value to the nearest whole number. Therefore, in this case, approximately 3 half-lives have occurred in the sample.