Problem preview

F-LE.3 Warmup M1-032-A11-V02

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 \(3\) and triples each step for \(3\) more steps to support a long-term comparison.

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The next three values are 9, 27, and 81 because tripling means multiply by 3 each step, which shows the outputs increasing very quickly over time.

The next three values are 6, 9, and 12 because the pattern goes up by 3 each step, which shows a steady increase over time.

The next three values are 9, 18, and 36 because tripling first gives 9 and then the pattern doubles, which shows the outputs increasing fast over time.

The next three values are 12, 48, and 192 because you keep multiplying by 4 each step, which shows the pattern growing quickly over time.

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Curriculum context

Course: Math I
Standard: F-LE.3
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Problem type: Extend exponential table values