Write and use an exponential rule
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
Original model:80 units increase 25% per interval for two intervals.
A percent change of r per interval uses factor 1+r for growth and 1−r for decay. The factor multiplies the current amount, so later absolute changes can differ.
Write and use an exponential rule — worked practice
A percent change of r per interval uses factor 1+r for growth and 1−r for decay. The factor multiplies the current amount, so later absolute changes can differ.
Original model:80 units increase 25% per interval for two intervals.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original model:80 units increase 25% per interval for two intervals. |
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1. 1. Convert
Write 25% as 0.25 and obtain the factor.
You should see: Growth factor 1.25.
2. 2. Apply once
Multiply 80 by 1.25.
You should see: First interval 100 units.
3. 3. Apply again
Multiply the new amount by 1.25.
You should see: Second interval 125 units.
4. 4. Check
Write one expression and explain the second increase.
You should see: 80×1.25^2=125; second increase 25 rather than 20.
What to finish
A two-interval percent-growth calculation with checked factors.
Watch for this
A fixed addition models linear change, not constant percentage growth.
How can I tell I understand it?
Explain why repeated percent growth differs from repeating the first absolute increase.
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. Exact topic chapters were opened in web result turn 325view 0–14.
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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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