Find doubling and halving intervals
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.
Want more background?
The idea in everyday life
Table for a model: day 0:18; day 1:27; day 2:40.5. A separate model: day 0:80; day 2:40; day 4:20.
A doubling or halving interval is the time needed for a repeated-factor model to change by a factor 2 or 0.5. A table can identify it without pretending that every exponential process doubles each interval.
Find doubling and halving intervals — worked practice
A doubling or halving interval is the time needed for a repeated-factor model to change by a factor 2 or 0.5. A table can identify it without pretending that every exponential process doubles each interval.
Table for a model: day 0:18; day 1:27; day 2:40.5. A separate model: day 0:80; day 2:40; day 4:20.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Table for a model: day 0:18; day 1:27; day 2:40.5. A separate model: day 0:80; day 2:40; day 4:20. |
Copy as plain text
1. 1. Compare factors
Find the first model factor.
You should see: 27/18=1.5, not 2.
2. 2. Inspect halving
Compare counts two days apart in the second model.
You should see: 80→40→20; halving interval 2 days.
3. 3. Predict
Extend the second rule two more days.
You should see: Day 6:10.
4. 4. Bound claim
Explain what the first short table establishes.
You should see: It supports factor 1.5 per day; exact doubling time is not an integer day shown.
What to finish
An interval identification and repeated-halving prediction.
Watch for this
A fifty-percent increase differs from a hundred-percent increase.
How can I tell I understand it?
Infer a repeated interval from the table without assuming one interval always equals one day.
Quick knowledge check
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