Compare growth and decay
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
Model A:64×1.5^t. Model B:64×0.5^t. Compare t=0,1,2.
Growth factors exceed 1; decay factors lie between 0 and 1. Decay removes a percentage of what remains, not the same original quantity each interval. A zero factor or negative factor is outside this introductory population/quantity model.
Compare growth and decay — worked practice
Growth factors exceed 1; decay factors lie between 0 and 1. Decay removes a percentage of what remains, not the same original quantity each interval. A zero factor or negative factor is outside this introductory population/quantity model.
Model A:64×1.5^t. Model B:64×0.5^t. Compare t=0,1,2.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Model A:64×1.5^t. Model B:64×0.5^t. Compare t=0,1,2. |
Copy as plain text
1. 1. Classify
Compare each factor with 1.
You should see: A grows; B decays.
2. 2. Calculate A
Apply 1.5 twice.
You should see: 64,96,144.
3. 3. Calculate B
Apply 0.5 twice.
You should see: 64,32,16.
4. 4. Interpret
Explain why B has not reached zero after two intervals.
You should see: Half of a positive remainder is positive.
What to finish
A growth/decay table with a positive-remainder explanation.
Watch for this
Repeated halving gives 16 after two intervals, not zero.
How can I tell I understand it?
Calculate a changed decay case without subtracting a fixed original loss.
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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. Exact topic chapters were opened in web result turn 325view 0–14.
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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