Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Select a usable window around a computed crossover
Problem
Let \(L(n)=100+10n\) and \(E(n)=5\cdot~2^n\). Compute \(\text{both}~\text{functions}\) at \(n=4\) and \(n=5\) to locate the first integer overtake. Which displayed window contains \(n=4,5\) and \(\text{all}~\text{four}~\text{outputs}\) without unnecessary vertical compression? Each graph panel is \(350~\text{pixels}\) high.
A useful crossover window must include evidence on both sides of the lead change while keeping that evidence visually separated. We’ll compute the bracketing inputs and outputs, test each window for inclusion, and compare vertical units per pixel to reject excessive compression.
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