Semi-Log Plots and Modelling

Making an exponential look straight.

12 problems · about 22 minutes · AP Precalculus 2.14, 2.15

NameDate

Figure — use these to answer the problems

On a semi-log plot an exponential becomes this straight line. Its slope is the log of the growth factor.

y = x + 1

Slope, which is log b1

Intercept, which is log a1

Figure 1

Straightforward practice. Get the method working first.

5 problems

A semi-log plot has intercept 2, so log a = 2. What is a?
Answer
2
What does a straight semi-log plot tell you?
- The underlying relationship is exponential.
- The underlying relationship is linear.
log a = 2. What is a?
Answer
log b = 1. What is b?
Answer
log a = 0. What is a?
Answer

The same ideas with more to keep track of.

3 problems

A semi-log plot curves rather than straightening. Is an exponential model right? 1 yes, 0 no.
Answer
Which plot straightens a power relationship? 1 semi-log, 2 log-log.
Answer
log y = 1 + 0.3x at x = 0. What is log y?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Match each plot with the relationship it straightens.
Draw a line from each item on the left to its match on the right.
- Plain plot of y against x
- Semi-log plot
- Log-log plot
- A linear relationship
- An exponential relationship
- A power relationship
log a = 3. What is a?
Answer
The Intercept
A semi-log plot has intercept 1, so log a = 1. What is a?
Answer
The Test
A semi-log plot is straight. Is an exponential model appropriate? 1 yes, 0 no.
Answer