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Grade 12 · unit review

Review: Exponential decay, uncertainty, and model inference

Apply half-life models, interpret probabilistic counts, and infer a rate from bounded evidence.

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Bring the unit skills together

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Unit review questions
1. A fictional amount starts at 64 units with half-life 6 h. What does the fixed-rate model give after 18 h?
2. After four half-lives, what percentage of the initial parent amount remains in the model?
3. Five independent parent nuclei each have 1/2 survival chance over one half-life. Which is accurate?
4. With no boundary transfers and a constant single-isotope model, readings at 0, 7, 14 h are 200, 100, 50 units. Which inference fits?

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Audit a fictional decay explanation for a museum display. Parent amounts at 0, 4, and 8 h are 120, 60, and 30 units, under a constant single-isotope model with no parent material entering or leaving except through decay. Infer half-life, predict amount and fraction at 12 h, and calculate the expected remaining count for a separate sample of three independent nuclei after two half-lives. Explain why another sample that is also leaking cannot support the same decay-only inference.

Work on paper or in your own document. Explain the choices you made.

  • Infer h = 4 h from both consecutive ratios.
  • Predict 15 parent units and 1/8 = 12.5% at 12 h.
  • For three nuclei after two half-lives, give expectation 3×1/4 = 0.75 and explain integer actual counts.
  • Identify leakage as a separate cause of reduced measured parent amount.
  • Describe parent transformation without claiming matter vanishes.
Compare with a model response

Both four-hour ratios are 1/2, so h = 4 h fits the stated model. At 12 h, three half-lives leave 120/8 = 15 parent units, or 12.5%. For three independent nuclei after two half-lives, each parent-survival chance is 1/4; expected count is 0.75, while each actual sample has an integer count. A leaking sample loses parent material by two processes, so the measured decline cannot isolate decay without accounting for removal. Parent nuclei transform; this is not a claim that matter vanishes.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.