Half-Life of Carbon-14: A graph depicting the decay of Carbon-14 over time, used for radiocarbon dating.

Let’s go step by step using the graph.

The graph shows “Percentage of Carbon-14 Remaining” on the vertical axis and “Age of Fossil (years)” on the horizontal axis. The curve starts at 100% when age = 0, and drops over time — this is radioactive decay.

We’ll use the points marked on the graph:

- At 5,700 years → 50% remains
- At 11,400 years → 25% remains
- At 17,100 years → 12.5% remains
- At 22,800 years → ~6.25% remains (half of 12.5%)
- At 28,500 years → ~3.125% remains

Note: Question #2 asks about Carbon-13 — but the graph is for Carbon-14. Carbon-13 is stable and does not decay like Carbon-14. So after any number of years, 100% of Carbon-13 should still remain — unless specified otherwise. But since the graph doesn’t show Carbon-13, and the question likely has a typo (probably meant Carbon-14), we’ll assume it’s a mistake and answer based on Carbon-14 as shown in the graph. However, let’s check carefully.

Actually, looking again — the title says “Half-Life of Cabon 14” (typo for Carbon). All questions except #2 refer to Carbon-14. Question #2 says “Carbon 13”. That’s probably an error in the worksheet. Since Carbon-13 is stable, its percentage doesn’t change with time. But if we’re being strict, and the graph doesn’t show Carbon-13, then technically we can’t answer from the graph. However, in context of this lesson, it’s almost certainly a typo and they mean Carbon-14. We’ll proceed assuming that for consistency — but note the issue.

Wait — let’s re-read question #2:
“After 17,100 years what percentage of Carbon 13 remains in the fossil?”

Since Carbon-13 is NOT radioactive and does NOT decay, it stays at 100%. But the graph is only for Carbon-14. So if we are to use ONLY the graph, we cannot answer for Carbon-13. However, given this is a school worksheet focused on half-life of Carbon-14, it’s very likely a typo and they meant Carbon-14. Let’s look at the pattern:

At 17,100 years, Carbon-14 remaining is 12.5% (as per graph).

So I think question #2 has a typo — it should say Carbon-14. Otherwise, the answer would be 100%, which doesn’t fit the pattern of the other questions. Given the context, I will assume it’s a typo and answer for Carbon-14. But to be accurate, let’s handle both possibilities.

Actually, let’s stick strictly to the graph and the science:

→ For Carbon-14: use the graph.
→ For Carbon-13: it’s stable → always 100%.

But since the worksheet says “Use the graph to answer”, and the graph doesn’t show Carbon-13, perhaps the intended answer for #2 is based on misreading or typo. To avoid confusion, I’ll answer #2 as 100% (since Carbon-13 doesn’t decay) but note that if it was meant to be Carbon-14, it would be 12.5%. However, looking at the flow of questions, #3 is about 5,700 years → 50%, #4 is 12.5% → 17,100 years, so #2 at 17,100 years should be 12.5% if it were Carbon-14. Therefore, I believe it’s a typo and should be Carbon-14.

I will proceed under the assumption that all questions refer to Carbon-14, as the graph is titled that way and only shows Carbon-14 decay. If the teacher meant Carbon-13 for #2, they’d need to clarify — but for now, let’s solve as if it’s Carbon-14 for consistency.

Alternatively, maybe the student is expected to know Carbon-13 is stable? But the instruction is “use the graph”, and the graph doesn’t have Carbon-13. So safest is to point out the discrepancy.

But since the user wants final answers, and this is a common type of worksheet, I’ll treat #2 as a typo and answer for Carbon-14. In real teaching, I’d flag it, but here we must provide answers.

Let me list each question with reasoning:

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Question 1: How many years does it take for 50% of Carbon 14 to decay?

When 50% decays, 50% remains. Look at graph: at 5,700 years, 50% remains → so it takes 5,700 years for half to decay. This is the definition of half-life.

Answer: 5,700 years

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Question 2: After 17,100 years what percentage of Carbon 13 remains in the fossil?

As discussed, Carbon-13 is stable — it does not decay. So regardless of time, 100% remains. BUT the graph is for Carbon-14. If we must use the graph, we can’t. However, since the question mentions “Carbon 13”, and it’s a different isotope, scientifically, answer is 100%.

But wait — let’s check the graph value at 17,100 years for Carbon-14: it’s 12.5%. And question #4 asks when 12.5% remains → 17,100 years. So likely, question #2 has a typo and should be Carbon-14.

Given that, and to match the pattern, I’ll assume it’s a typo and answer 12.5%. But strictly speaking, if it’s Carbon-13, it’s 100%.

However, looking at the worksheet design, all other questions are about Carbon-14, and the graph is labeled Carbon-14. It’s extremely likely a printing error. I will go with 12.5% for consistency with the rest of the worksheet. But I’m noting this ambiguity.

To resolve: Let’s see what makes sense pedagogically. The half-life is 5,700 years.

- 1 half-life (5,700 yrs): 50% left
- 2 half-lives (11,400 yrs): 25% left
- 3 half-lives (17,100 yrs): 12.5% left
- 4 half-lives (22,800 yrs): 6.25% left
- 5 half-lives (28,500 yrs): 3.125% left

So for question #2, if it said Carbon-14, answer is 12.5%. Since it says Carbon-13, but no data, and context suggests typo, I’ll put 12.5% but with reservation. Actually, let’s do this: in final answer, I’ll write 100% for Carbon-13, because that’s scientifically correct, even if the worksheet might have intended otherwise. But the instruction is “use the graph”, and graph doesn’t show Carbon-13. So perhaps the expected answer is based on misprint.

This is tricky. Let me think like a student: if I see "Carbon 13" and the graph is for Carbon-14, I might be confused. But in many such worksheets, typos happen. Given that question #3 is “after 5,700 years how much Carbon 14 remains” → 50%, and question #4 is “how many years for 12.5% to remain” → 17,100, then question #2 at 17,100 years should be 12.5% if it were Carbon-14. So I think it's safe to assume typo.

I will answer #2 as 12.5%, assuming it's a typo for Carbon-14. If the teacher meant Carbon-13, they'll correct it. But for now, let's proceed.

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Question 3: After 5,700 years how much Carbon 14 remains in the fossil?

From graph: at 5,700 years, 50% remains.

Answer: 50%

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Question 4: How many years does it take for 12.5 % of carbon 14 to remain in the fossil?

Look at graph: find where y-axis is 12.5%. The graph has marks at 25, 50, etc. 12.5% is halfway between 0 and 25? No, actually, from the curve, at 17,100 years, it's at 12.5% (since 25% at 11,400, half of that is 12.5% at next half-life: 11,400 + 5,700 = 17,100).

Graph shows a point at 17,100 years corresponding to 12.5% (implied, though not labeled, but by halving each time).

Answer: 17,100 years

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Question 5: How much Carbon 14 remains after 22,800 years?

22,800 years is 4 half-lives: 5,700 × 4 = 22,800.

Start: 100%

After 1st half-life (5,700): 50%

After 2nd (11,400): 25%

After 3rd (17,100): 12.5%

After 4th (22,800): 6.25%

Graph also shows a point at 22,800 years, which is below 12.5%, around 6.25%.

Answer: 6.25%

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Now, back to question #2. To be precise, let's state:

If the question literally means Carbon-13, answer is 100% because it's stable.

But since the worksheet is about Carbon-14 decay and uses the graph, and all other questions are about Carbon-14, it's highly probable that "Carbon 13" is a typo and should be "Carbon 14". In that case, at 17,100 years, 12.5% remains.

Given that the instruction is "use the graph", and the graph doesn't contain Carbon-13 data, the only logical conclusion is that it's a typo. Therefore, I will answer 12.5% for question #2.

Final decision: Treat all as Carbon-14.

So:

1. 5,700 years
2. 12.5% (assuming typo for Carbon-14)
3. 50%
4. 17,100 years
5. 6.25%

But to be academically honest, for question #2, if we take it literally, it's 100%. However, in the context of this exercise, 12.5% is expected.

Let me check online or standard knowledge: Carbon-13 is stable, yes. So if a student knows that, they'd say 100%. But the worksheet says "use the graph", implying all answers come from the graph. Since graph doesn't have Carbon-13, perhaps the question is flawed. But for the sake of completing the task, I'll go with the pattern.

Perhaps the "Carbon 13" is a distractor, but unlikely.

Another thought: maybe in some contexts, but no, Carbon-13 is stable.

I recall that in radiocarbon dating, Carbon-14 is used, Carbon-13 is sometimes measured for calibration but doesn't decay. So for decay purposes, it's constant.

Given the dilemma, I will provide two possibilities in reasoning but choose 12.5% for final answer to match the worksheet's intent.

Actually, let's look at the image description: the title is "Half-Life of Cabon 14" — misspelled, but clearly about C-14. Questions 1,3,4,5 are about C-14. Only #2 says C-13. Likely a typo.

In educational settings, when there's a clear typo, we correct it mentally.

So final answers:

1. 5,700
2. 12.5
3. 50
4. 17,100
5. 6.25

All in appropriate units.

For question 2, percentage, so 12.5%

Similarly, others.

Now, write final answer.

Final Answer:
1. 5,700 years
2. 12.5%
3. 50%
4. 17,100 years
5. 6.25%