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F-LE.3 Warmup M2-026-A09-V04

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

Use model comparison to answer a decision context

Problem

Compare the programs at \(w=3\). Substitute \(3\) into the complete quadratic expression for \(A\), evaluate \(2^3\) before multiplying by \(20\) for \(B\), and compare the outputs without assuming exponential models are always larger.

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Program B, because 20(2)³=240, which is greater than 175.

The two programs cannot be compared because one model is quadratic and the other is exponential.

Program A, because FA(3)=175 and FB(3)=160.

Program B, because exponential models are always larger than quadratic models.

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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: Use model comparison to answer a decision context