Study Guide
Learning Objectives
- Use a semi-log plot to decide if an exponential model fits (2.15.A.1).
- State the advantage vs adding a constant to $y$ (2.15.A.2).
- Construct a linearization of exponential data on a semi-log graph (2.15.B.1).
- Relate $y=ab^{x}$ to $\log_n y=(\log_n b)x+\log_n a$ (2.15.B.2).
Suggested Practice Sequence
1. Define semi-log: one axis log-scaled. 2. Sketch/interpret: exponential $\to$ linear on log-$y$. 3. Decide appropriate model from a described plot. 4. From two linearized points, find slope $=\log_n b$ and intercept $=\log_n a$. 5. Recover $a$ and $b$; write $y=ab^{x}$. 6. Explain the "no added constant" advantage (2.15.A.2).
Classroom / Check-In Moves
- Same table: linear plot vs semi-log plot card compare.
- "Slope on semi-log means ___ for the base."
- Recover $a,b$ exit tickets.
Misconception Watch-List
- Thinking any curved scatter is exponential.
- Mixing log-$x$ (often for power models) with log-$y$ (exponential).
- Reporting $\log a$ as $a$ without exponentiating.
- Ignoring base $n$ of the log scale used.
Vocabulary to Own
- semi-log plot
- logarithmically scaled axis
- linearization
- exponential characteristics
- rate of change on semi-log ($\log_n b$)
- initial linear value ($\log_n a$)
Materials Map
- Practice: recognize and linearize
- Word: data/context model decisions
- Mixed / multi-*: link to 2.5–2.6 modeling and 2.4–2.5 exponential form
- Review & practice test: decide + recover $a,b$
- Interactive: plot meaning and parameter recovery