Semi-log Plots
A semi-log plot puts y on a logarithmic axis and leaves x alone, so equal vertical steps mean equal factors: the gridlines 1, 10, 100, 1000 sit equally spaced. Exponential data, and only exponential data, becomes a straight line there, because log(a·b^x) = log(a) + x·log(b) is literally linear. The slope encodes the growth factor and the intercept the initial value, so the plot is both a test for exponential structure and a tool for recovering the model.
The mistakes are all axis misreads: calling data linear because its semi-log plot is a line, treating a gridline step as an added amount instead of a multiplied factor, and expecting the plot to straighten every dataset (linear data actually bends on it). The lesson drills the reads in both directions.
The work
3 ways in · any order
Lesson
Semi-log Plots
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Up means times on a log axis: the lesson shows why exponentials straighten on semi-log plots, how slope and intercept give back the growth factor and initial value, what linear data looks like there, and closes with ten scenarios of reading, recovering, and diagnosing models from the plot.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 2.15 misconceptions: reading a straight semi-log line as linear growth, and treating equal steps on the log axis as equal amounts instead of equal factors. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.