Analyze the table for \(n=0,1,2,3\). Compute consecutive differences for \(L\) and consecutive ratios for \(E\), record the leader or tie at each listed \(n\), then extend \(\text{both}~\text{patterns}\) to \(n=4\) and identify the first overtake after the table.

Growth patterns reveal themselves through different invariants: constant differences for linear models and constant ratios for exponential models. We’ll identify both patterns, compare corresponding rows for leads or ties, and extend each rule one step to locate the first reversal.