Cogito
AP Precalculus · Chapter 5 · Lesson 3
Semi-Log Plots and Modelling
Making an exponential look straight.
12 problems · about 22 minutes · AP Precalculus 2.14, 2.15
What this lesson teaches
The student uses semi-log plots to identify exponential relationships and builds models from data.
- A semi-log plot logs y and straightens an exponential relationship.
- Its slope is log b and its intercept is log a.
- A log-log plot straightens a power relationship instead.
Warm Up
Straightforward practice. Get the method working first.
5 problemsA semi-log plot has intercept 2, so log a = 2. What is a?
Answer 100
Why 100.
What does a straight semi-log plot tell you?
Answer The underlying relationship is exponential.
Why An exponential relationship.
log a = 2. What is a?
Answer 100
Why 10².
log b = 1. What is b?
Answer 10
Why 10¹.
log a = 0. What is a?
Answer 1
Why 10⁰.
Build It Up
The same ideas with more to keep track of.
3 problemsA semi-log plot curves rather than straightening. Is an exponential model right? 1 yes, 0 no.
Answer 0
Why Only a straight one confirms it.
Which plot straightens a power relationship? 1 semi-log, 2 log-log.
Answer 2
Why Both axes logged.
log y = 1 + 0.3x at x = 0. What is log y?
Answer 1
Why The intercept.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each plot with the relationship it straightens.
Answer Plain plot of y against x → A linear relationship; Semi-log plot → An exponential relationship; Log-log plot → A power relationship
Why Count how many axes are logged.
log a = 3. What is a?
Answer 1000
Why 10³.
The Intercept: A semi-log plot has intercept 1, so log a = 1. What is a?
Answer 10
Why 10.
The Test: A semi-log plot is straight. Is an exponential model appropriate? 1 yes, 0 no.
Answer 1
Why Yes.