Identify exponential baselines, construct and fit logarithmic responses, and use transformed inverses with explicit domains. School algebra and graph reading suffice; this is a focused extension, not complete AP preparation.
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A baseline changes raw ratios, so a shifted model needs a different diagnostic.
For equally spaced inputs, y=k+A b^t has a constant ratio after subtracting k. Differences between successive outputs also form a geometric pattern when the model is nonconstant. Raw ratios need not be constant.
Inverses and inequalities must preserve the original domain.
For log base b of u, require u>0, b>0 and b≠1. A base between zero and one is valid but reverses order. Keep these restrictions when rewriting equations.
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Exponential and logarithmic evidence: mixed practice
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Use equal-step differences to recover a baseline, then check a prediction in original units.
6 practice tasks.
Fit a log-input response and distinguish its original-scale residual evidence from other transformations.
7 practice tasks.
Recover full inverse rules and solve inequalities using the correct monotonic direction.
6 practice tasks.
