Safety and evidence boundary
Use supplied long-term ecological datasets and low-risk simulations. Do not manipulate wild populations, introduce species, enter unsafe field sites, or infer a single cause from correlation alone. Population models are approximations with explicit scale and boundary assumptions.
Explicit science instruction
In an exponential model, population change is proportional to current population size. In continuous form dN/dt=rN; in discrete contexts growth can be represented by repeated multiplication. Exponential growth can describe short intervals with abundant resources but rarely persists indefinitely.
Vocabulary: population size; growth rate; per-capita rate; exponential; doubling time; birth; death; immigration; emigration.
Worked example with reasoning
A fictional population grows 10% per interval from N=100: 110, 121, 133.1... The absolute increase grows because the same proportion acts on a larger base.
Guided question
Why does constant percent growth produce increasing absolute additions?
Independent work
- Calculate five intervals at 5% growth.
- Graph N over time.
- Compare absolute and percent change.
- State two assumptions.
Misconception check
Exponential does not mean “fast” in every interval; it describes proportional growth structure.
Formative understanding check
100 organisms growing 20% gives how many after one interval?
Worked response
120.
Open-book formative practice only; not an official mastery attempt or grade.
Mentor evidence conference
Ask Archaemenes to challenge your systems model, quantitative interpretation, alternative explanations, and boundary conditions.
Open ArchaemenesTeacher guidance
Foundation: use repeated-percent tables. Core: calculate and graph. Extended: connect r to doubling time conceptually.
Preserve learning evidence
Keep models, calculations, graphs, corrections and uncertainty notes in the matching Week 33 evidence field.