Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Compare quadratic and exponential table growth
Problem
Analyze \(Q\) and \(E\) by computing \(Q\)'s first and second differences and \(E\)'s consecutive ratios. Record the leader or tie at \(n=1\) through \(4\), extend \(\text{both}~\text{patterns}\) to \(n=5\), and identify the post-table leader.
Quadratic and exponential tables can cross more than once, so early leadership does not settle long-run growth. We’ll use first and second differences to identify the quadratic, ratios to identify the exponential, track every listed comparison, and extend both established rules beyond the last tie.
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