Construct and read logarithmic vertical axes, recover exponential models, and compare baseline assumptions using original-scale errors and unused predictions.
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Logarithmic axes represent ratios rather than equal additive differences.
The base-ten logarithm increases by one: log₁₀(10u)=1+log₁₀u for u>0. Equal distances on a base-ten logarithmic axis therefore represent equal factors, not equal additions.
A baseline changes what belongs on a logarithmic axis.
In y=k+A b^x, the excess y−k is proportional across equal x steps. Taking log(y) generally does not remove the additive k. Subtracting a proposed baseline is a modeling decision that still needs evidence.
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Semilog modeling: mixed practice
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Make the axis transformation visible, recover a response rule and evaluate what a straight-looking fit actually supports.
8 practice tasks.
