Higher Tier: interacting factors and greenhouse decisions
| English | 中文 | Pinyin |
|---|---|---|
| limiting factor/ˈlɪmɪtɪŋ ˈfæktə/ | 限制因素 | xiàn zhì yīn sù |
| inverse-square relationship/ɪnˈvɜːs skweə rɪˈleɪʃənʃɪp/ | 平方反比关系 | píng fāng fǎn bǐ guān xì |
What would explain this observation?
- Higher Tier: A greenhouse can spend more on lighting without growing more crop. A useful decision checks which factor limits the response and whether extra revenue exceeds extra cost.
- Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
Build the model
- Photosynthesis factors interact: light, carbon dioxide or temperature can limit rate under a particular set of conditions. Increasing a factor that is not currently limiting may produce no gain. On a graph, compare curves at the same value of the horizontal variable and use the stated changed condition to explain differences.
- limiting factor 限制因素: A condition whose shortage restricts the process rate; inverse-square relationship 平方反比关系: A relationship in which a quantity varies as one divided by distance squared.
What does doubling distance do to ideal point-source light intensity?
For the ideal point-source model, light intensity is proportional to 1/distance². Doubling distance makes intensity one quarter, not one half. Real lamp geometry and reflections can depart from this approximation. A greenhouse decision compares added revenue with added lighting, heating or carbon dioxide costs; maximum photosynthesis rate need not give maximum profit.
Match each technical term to its precise meaning.
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For the ideal point-source model, light intensity is proportional to 1/distance². Doubling distance makes intensity one quarter, not one half. Real lamp geometry and reflections can depart from this approximation. A greenhouse decision compares added revenue with added lighting, heating or carbon dioxide costs; maximum photosynthesis rate need not give maximum profit.
- Inspect supplied curves with one controlled change between them. Identify evidence that a proposed limiting factor matters at a particular point. Calculate relative intensity using a stated reference distance, then evaluate a fictional greenhouse budget. These calculations extend RP6 interpretation but do not justify uncontrolled heating or added gases in a classroom.
Which two habits make the investigation or model in this case more defensible?
Inspect supplied curves with one controlled change between them. Identify evidence that a proposed limiting factor matters at a particular point. Calculate relative intensity using a stated reference distance, then evaluate a fictional greenhouse budget. These calculations extend RP6 interpretation but do not justify uncontrolled heating or added gases in a classroom.
Work from known quantities
- State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
- Known: intensity is 100 relative units at 20 cm. At 40 cm the ideal model predicts 100×(20/40)² = 25. Separately, a greenhouse change adds 180 revenue units but 120 cost units, so added profit is 60. A second change adding 40 revenue and 70 cost reduces profit by 30 even if photosynthesis increases.
Intensity is 144 units at 10 cm. Calculate ideal intensity at 30 cm. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
Intensity is 144 units at 10 cm. Calculate ideal intensity at 30 cm.
The result is 16 relative units. Known: intensity is 100 relative units at 20 cm. At 40 cm the ideal model predicts 100×(20/40)² = 25. Separately, a greenhouse change adds 180 revenue units but 120 cost units, so added profit is 60. A second change adding 40 revenue and 70 cost reduces profit by 30 even if photosynthesis increases.
Check the conclusion and its limits
- Inverse square applies to light intensity in the stated model, not automatically to photosynthesis rate across all conditions. A plateau can reflect another limiting factor. Profit uses both income and cost; comparing income alone is insufficient.
- Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
Maximum photosynthesis rate must always give maximum profit. This claim is false: Inverse square applies to light intensity in the stated model, not automatically to photosynthesis rate across all conditions. A plateau can reflect another limiting factor. Profit uses both income and cost; comparing income alone is insufficient.
Higher Tier: interacting factors and greenhouse decisions: For the ideal point-source model, light intensity is proportional to 1/distance². Doubling distance makes intensity one quarter, not one half. Real lamp geometry and reflections can depart from this approximation. A greenhouse decision compares added revenue with added lighting, heating or carbon dioxide costs; maximum photosynthesis rate need not give maximum profit.
Maximum photosynthesis rate must always give maximum profit.
Inverse square applies to light intensity in the stated model, not automatically to photosynthesis rate across all conditions. A plateau can reflect another limiting factor. Profit uses both income and cost; comparing income alone is insufficient.
A condition whose shortage restricts the process rate: write the technical term.
limiting factor means A condition whose shortage restricts the process rate.