Infer a Half-life and Check a Claim
Use ratios and intervals to assess an exponential-model explanation.
Supplied materials
- Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.
Learn the idea
A model can be inferred from a pattern, but its assumptions must be checked. If a parent amount halves in a measured interval, that interval is consistent with a half-life under a constant-rate, single-isotope model. Repeated ratios strengthen the fit. If material is also leaking out or being added, declining measured parent amount cannot isolate radioactive decay alone.
Supplied fictional amount record: at 0, 5, and 10 hours, parent amounts are 96, 48, and 24 units. Each five-hour ratio is 1/2, consistent with h = 5 h. The fitted model predicts 12 units at 15 h. A separate record of 96 → 48 includes both decay and an unknown outward material transfer; that one decrease cannot determine a decay half-life without more information. These are mathematical cases, not dating or safety advice.
- Divide 48 by 96 and 24 by 48.
- Associate the repeated half ratio with each five-hour interval.
- Predict the next amount under the no-transfer, constant-rate model.
- Explain why the separate unknown-transfer record cannot isolate the decay rate.
See the method in action
Two consecutive five-hour ratios equal 1/2, fitting h = 5 h and predicting 96×(1/2)³ = 12 units at 15 h. With unknown leakage, the same observed decline could combine decay and removal in different proportions.
Check your reasoning
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See the answer and explanation
The decrease cannot isolate a radioactive half-life because removal also changed the amount.
The measured decrease has two possible contributors. The decay-only inference requires the stated no-addition and no-removal assumptions.
Take it further
Change the no-transfer record to 96, 72, and 54 units at equal five-hour intervals. The ratio is now 3/4 each time, not 1/2; five hours is not the half-life. The fitted next five-hour amount is 54×3/4 = 40.5 units.
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