F20 · Topic 3.17
Growth laboratory
1. Predict first
Predict the effect of doubling n from 8 to 16 on n, n² and 2ⁿ.
Change it · step through · explain
Change an input, predict what will happen, then advance one step. Read why the state changes, reset and experiment. This fixed teaching model does not save progress or award XP.
Ready · Make a prediction
- Input 18Waiting
Ready to experiment
Why: Predict the first change, then advance one step.
Try this: Compare n=4, 8 and 16. Read exact labels when a small bar becomes hard to see.
2. Build your procedure
Write one linear and one quadratic loop and identify the counted body operation. Explain why two separate loops are not equivalent to nested loops.
Use AP CSP pseudocode, a language you know, or precise plain language. Your code is not executed here. Use the classroom assignment to save your response.
3. Check boundaries
| Input | Expected | Why this case |
|---|---|---|
| n4 | linear 4; quadratic 16; exponential 16 | Equal small counts do not establish equal growth. |
| n8 | 8;64;256 | Separate the curves. |
| n16 | 16;256;65,536 | Exponential growth dominates asn increases. |
4. Explain and reflect
Why does this count table not predict seconds on every machine?
Model limits: Counts are calculated formulas for bounded input sizes, not timings and not execution of arbitrary student algorithms.