Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Audit a growth claim outside its graph window
Problem
Audit any long-run conclusion drawn from the graph on \(0\le~t\le~4\). Verify the ordering at \(t=4\), extend \(\text{both}~\text{formulas}\) to \(t=10\), and explain why a window ending before the crossover cannot establish the eventual ordering.
A graph window supports claims only over the inputs it actually displays. We’ll verify the ordering at its boundary, extend both formulas to the same later input, and use any reversal to test whether the visible trend justifies a long-run conclusion.
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