The columns labeled "Fraction remaining" and "Percentage remaining" in the chart represent the "amount of material that has not decayed."
Let's break this down step-by-step:
1. Half-lives Elapsed: This column shows the number of half-lives that have passed. A half-life is the time required for half of the radioactive material to decay.
2. Fraction Remaining: This column indicates the fraction of the original material that remains un-decayed after a certain number of half-lives.
- At 0 half-lives elapsed, the fraction remaining is [tex]\( \frac{1}{1} = 1 \)[/tex], meaning 100% of the material is still present.
- At 1 half-life elapsed, the fraction remaining is [tex]\( \frac{1}{2} = 0.5 \)[/tex], meaning 50% of the material is still present.
- At 2 half-lives elapsed, the fraction remaining is [tex]\( \frac{1}{4} = 0.25 \)[/tex], meaning 25% of the material is still present.
- This pattern continues, decreasing by half for each additional half-life elapsed.
3. Percentage Remaining: This column shows the same information as the "Fraction remaining" column but in percentage form.
- At 0 half-lives elapsed, 100% of the material remains.
- At 1 half-life elapsed, 50% of the material remains.
- At 2 half-lives elapsed, 25% of the material remains.
- This pattern continues, decreasing by half for each additional half-life elapsed.
Therefore, the values in the "Fraction remaining" and "Percentage remaining" columns measure how much of the original material has not yet decayed over time.
Thus, the correct answer is "amount of material that has not decayed."
