Distinguish additive and multiplicative change
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
Practice populations A:20,30,40,50 and B:20,40,80,160 at days 0,1,2,3.
Linear change adds the same amount in equal intervals; exponential change multiplies by the same factor. “Fast” alone does not identify an exponential process.
Distinguish additive and multiplicative change — worked practice
Linear change adds the same amount in equal intervals; exponential change multiplies by the same factor. “Fast” alone does not identify an exponential process.
Practice populations A:20,30,40,50 and B:20,40,80,160 at days 0,1,2,3.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Practice populations A:20,30,40,50 and B:20,40,80,160 at days 0,1,2,3. |
Copy as plain text
1. 1. Differences
Calculate each successive difference in A.
You should see: Differences 10,10,10.
2. 2. Ratios
Divide each B count by its preceding count.
You should see: Ratios 2,2,2.
3. 3. Models
Write a rule for each sequence.
You should see: A(t)=20+10t; B(t)=20×2^t.
4. 4. Interpret
Compare day-three changes without equating growth speed with mechanism.
You should see: A has added 30; B has multiplied by 8.
What to finish
Two sequence models with difference and ratio comparisons.
Watch for this
The interval is the same; the change rule is multiplication.
How can I tell I understand it?
Classify a changed sequence by its mechanism rather than its apparent speed.
Quick knowledge check
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