Problem preview

F-LE.3 Core M2-026-R05-V02

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

Compare repeated multiplication with power growth

Problem

Classify the \(E\) and \(P\) patterns by computing \(E\)'s consecutive output ratios and \(P\)'s first differences. Relate the constant ratio to the variable exponent in \(5\cdot~3^n\) and the nonconstant differences to the cubic input power in \(5(n+1)^3\).

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E is exponential with factor 3; P is cubic with first differences 35,95,185.

E is polynomial because it uses repeated multiplication.

P has output ratios 35,95,185.

E has first differences 3,3,3.

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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