Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Compare repeated multiplication with power growth
Problem
Classify the \(\text{two}~\text{table}~\text{patterns}\) without relying on shared outputs. Compute consecutive ratios for \(E\) and first differences for \(P\), connect the constant factor to \(3\cdot~2^n\) and the changing differences to \(3n^{2}\), and state the growth family of each.
Shared outputs do not make two growth patterns the same, because classification depends on how each row changes. We’ll compare consecutive ratios with first and second differences, then connect those numerical signatures to repeated multiplication and a fixed power of the input.
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