Common Mistakes

Frequent Errors

1. Using a linear model when successive ratios are constant. 2. Setting $b$ equal to the percent (e.g., 5% growth as $b=0.05$ instead of $b=1.05$). 3. Misidentifying $a$ when the scenario does not start at $t=0$. 4. Ignoring a vertical shift/baseline before checking ratios (2.5.A.2). 5. Wrong base when converting daily vs weekly growth. 6. Solving two-point systems with arithmetic instead of exponential structure. 7. Treating regression output as exact without contextual sense-check. 8. Extrapolating far beyond data without noting limitations (2.5.B.3).

Why These Happen

Students default to linear slope ideas and treat "$b$" as a percent label rather than a multiplicative factor per unit.

How to Fix Them

• Ratio table every time before choosing model type.
• Sentence template: "$b$ is the factor we multiply by each [unit]."
• For offsets: subtract baseline, check ratios, then add back in the model.
• Rewrite with 2.4 skills when units change.

Avoidance Scripts

• "Constant difference $\rightarrow$ linear; constant ratio $\rightarrow$ exponential."
• "5% growth per year means multiply by 1.05 each year."
• "Prediction is only as good as the domain and assumptions."

Quick Self-Check

• Did I interpret $a$ and $b$ in context?
• Is $b$ a growth factor (not just a percent)?
• Did I note domain limits on predictions?