Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Extend exponential table values
Problem
Extend the pattern that starts at \(4\) and doubles each step for \(4\) more steps to support a long-term comparison.
Big Picture
What this problem is really about
Doubling preserves a constant multiplier, not a constant amount added. We’ll apply the factor to each newly produced value for the required number of steps, then verify the continuation with consecutive ratios. Comparing the absolute increases afterward will show how a fixed exponential factor produces larger and larger gains over time.
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