Evaluate competing predictions
See this course’s project requirements
A population and cooling model sheet comparing repeated addition with repeated multiplication and checking predictions against supplied observations.
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What to include
- Compare a linear and an exponential sequence.
- Show repeated-factor tables and direct formulas.
- Check two growth and two decay calculations.
- Explain a doubling or halving interval from supplied data.
- Compare a model with observations and retain its mismatch.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Supplied observations at t=0,1,2,3 are 10,20,40,75. Candidates L=10+10t and E=10×2^t.
A model should be chosen by its mechanism and evidence, not by the larger predicted value. Compare observed and predicted values at the same inputs, and state whether a finite table can establish a universal rule.
Evaluate competing predictions — worked practice
A model should be chosen by its mechanism and evidence, not by the larger predicted value. Compare observed and predicted values at the same inputs, and state whether a finite table can establish a universal rule.
Supplied observations at t=0,1,2,3 are 10,20,40,75. Candidates L=10+10t and E=10×2^t.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Supplied observations at t=0,1,2,3 are 10,20,40,75. Candidates L=10+10t and E=10×2^t. |
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1. 1. Compute predictions
Build predictions for both models.
You should see: L:10,20,30,40; E:10,20,40,80.
2. 2. Compare observations
Find absolute errors at t=2 and 3.
You should see: L errors 10,35; E errors 0,5.
3. 3. Choose cautiously
Explain which better fits these later observations.
You should see: E fits better here, but the last value differs by 5.
4. 4. Assemble
Write a bounded conclusion with a next-check question.
You should see: Exponential growth is a useful short model; ask whether resource limits affect later counts.
What to finish
A prediction-error comparison and bounded model conclusion.
Watch for this
A finite short fit does not guarantee future behavior.
How can I tell I understand it?
Choose a better short model without treating a finite fit as a permanent law.
Quick knowledge check
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Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
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