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F-LE.3 Core M2-026-R05-V03

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

Compare repeated multiplication with power growth

Problem

Classify \(\text{both}~\text{decay}~\text{patterns}\) by computing consecutive output ratios. Verify \(E\)'s constant ratio and \(P\)'s ratios \(1/4\), \(4/9\), and \(9/16\), then connect the results to exponential decay versus reciprocal-square power decay.

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P has first differences 1/4,4/9,9/16.

E is polynomial decay because it decreases.

E is exponential decay with ratio 0.5; P is reciprocal-square decay with ratios 1/4,4/9,9/16.

E has first differences 0.5,0.5,0.5.

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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 repeated multiplication with power growth