Test a model outside its useful range
See this course’s project requirements
A linear-model comparison with tables, graphs, slope and intercept interpretations, a solved intersection and a limitation note.
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What to include
- Include input/output definitions and bounded domains.
- Provide checked tables and labeled linear graphs.
- Interpret rate and starting output with units.
- Solve an intersection and verify both outputs.
- Document a capacity-limited model and all changed-case checks.
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 case: V(t)=10+5t for 0≤t≤6. The container capacity is 40 L, and inflow stops at capacity. Observations at t=0,2,4,6 are 10,20,30,40 L.
A mathematical rule can be evaluated where its real mechanism no longer works. Distinguish calculation from supported prediction and revise the domain when capacity or a changed process invalidates the model.
Test a model outside its useful range — worked practice
A mathematical rule can be evaluated where its real mechanism no longer works. Distinguish calculation from supported prediction and revise the domain when capacity or a changed process invalidates the model.
Original case: V(t)=10+5t for 0≤t≤6. The container capacity is 40 L, and inflow stops at capacity. Observations at t=0,2,4,6 are 10,20,30,40 L.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: V(t)=10+5t for 0≤t≤6. The container capacity is 40 L, and inflow stops at capacity. Observations at t=0,2,4,6 are 10,20,30,40 L. |
Copy as plain text
1. 1. Check supplied observations
Evaluate the rule at each observed time.
You should see: 10,20,30,40 L agree with the observations.
2. 2. Find the limit
Solve 10+5t=40.
You should see: t=6 minutes is capacity.
3. 3. Audit extrapolation
Calculate the rule at t=8 and compare to the stated mechanism.
You should see: The formula gives 50 L, exceeding 40 L; continued linear inflow is unsupported.
4. 4. Write the revised explanation
State what is known after capacity without inventing extra mechanism.
You should see: The original linear rule ends at minute six; inflow stops, so the supplied case remains 40 L.
What to finish
A capacity-limited model review with a revised post-limit explanation.
Watch for this
A changed mechanism requires a new rule, not silent continuation.
How can I tell I understand it?
Revise a model when its mechanism changes rather than changing observations to fit it.
Quick knowledge check
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