Problem preview
F-LE.3 Warmup M1-032-A02-V01

Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.

Compare quadratic and exponential values over the same inputs

Problem

Use the displayed table to compare \(Q\) and \(E\) at every listed input, identify every tie, and describe how dominance changes across the inputs.

Big Picture

What this problem is really about

Quadratic and exponential values can trade places more than once over a short input range, so growth type alone does not settle every row. We’ll compare the two outputs at each matching input, record equalities as genuine ties, and track the sign of their difference. That complete sequence shows exactly where dominance changes without forcing a single-crossing story onto the data.

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Four variants of this problem type
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
Compare quadratic and exponential values over the same inputs