Study Guide
Learning Objectives
- Recognize contexts suited to logarithmic models (2.14.A.1).
- Construct models from proportion + zero, two pairs, or transforms of $a\log_b x$ (2.14.A.2–A.3).
- Use technology logarithmic regression when appropriate (2.14.A.4).
- Prefer $\ln$ when natural for the context (2.14.A.5).
- Predict dependent values from a fitted model (2.14.A.6).
Suggested Practice Sequence
1. Identify equal output intervals vs proportional inputs. 2. Build $y=a\log_b x$ from two points (or proportion + intercept idea). 3. Apply shifts/stretches: $a\log_b(x-h)+k$. 4. Technology: log regression; report equation. 5. Predict $y$ for a given $x$; check Dom. 6. Interpret parameters in a short sentence.
Classroom / Check-In Moves
- "Exp vs log vs linear — which story?" card sort.
- Two-point fit races (no calculator, then with).
- Prediction + Dom check ritual.
Misconception Watch-List
- Treating log models as always increasing past Dom.
- Mixing up which variable is logged in regression.
- Predicting outside the data range without caution.
- Forgetting units on predictions.
Vocabulary to Own
- logarithmic model; proportional growth (input)
- real zero (of the model context)
- input-output pair
- transformation of $a\log_b x$
- logarithmic regression
- natural logarithm ($\ln$)
- prediction / dependent variable
Materials Map
- Practice: construct and predict
- Word: contextual modeling stories
- Mixed / multi-*: link to 2.11–2.13 features/equations
- Review & practice test: construct + predict fluency
- Interactive: model choice and prediction