To determine what is being measured in the columns labeled "Fraction remaining" and "Percentage remaining" in the chart, let's analyze the information provided:
The chart shows a series of half-lives elapsed and corresponding values for the "Fraction remaining" and "Percentage remaining." These values represent how much of a given material remains after each half-life:
1. Half-lives elapsed: This is a measure of time, quantified in terms of the number of half-lives. A "half-life" is the time required for a quantity to reduce to half its initial value.
2. Fraction remaining: This shows the fraction of the initial amount of material that remains after each half-life. For example:
- After 0 half-lives, the fraction remaining is [tex]\( \frac{1}{1} \)[/tex].
- After 1 half-life, the fraction remaining is [tex]\( \frac{1}{2} \)[/tex].
- After 2 half-lives, the fraction remaining is [tex]\( \frac{1}{4} \)[/tex], and so on.
3. Percentage remaining: This represents the same information as the Fraction remaining, but as a percentage of the original amount:
- After 0 half-lives, the percentage remaining is 100%.
- After 1 half-life, the percentage remaining is 50%.
- After 2 half-lives, the percentage remaining is 25%, and so forth.
From this analysis, it is clear that both columns ("Fraction remaining" and "Percentage remaining") indicate how much of the initial material is still present and hasn't decayed over the course of the elapsed half-lives.
Therefore, the value being measured in the columns labeled "Fraction remaining" and "Percentage remaining" is:
amount of material that has not decayed
