Problem preview

F-LE.3 Warmup M2-026-A03-V03

Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.

Compare exponential and polynomial growth from a graph

Problem

Polynomial model: \(P(x)=x^3\); Exponential model: \(E(x)=1.2^x\). Graph description: The cubic is higher across the shown window. What comparison about their growth is supported?

Answer choices

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x³ grows faster than 1.2ˣ because it is above it everywhere on the graph shown.

x³ and 1.2ˣ grow at the same rate since both increase as x increases.

The graph proves that x³ will always stay above 1.2ˣ for all x.

The graph window may be too small to show when 1.2ˣ eventually overtakes x³.

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Curriculum context

Course: Math II
Standard: F-LE.3
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Problem type: Compare exponential and polynomial growth from a graph