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F-LE.3 Core M2-026-R10-V02

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

Audit a growth claim outside its graph window

Problem

Audit the claim that \(Q\) and \(E\) have equal growth because \(\text{both}\) equal \(16\) at \(n=4\). Distinguish equality at \(\text{one}~\text{input}\) from equality of functions, evaluate \(Q(8)\) and \(E(8)\), and use the out-of-window comparison to assess the claim.

Source comparison of Q(n)=n² and E(n)=2^n for n=1,2,3,4, where Q values are 1,4,9,16 and E values are 2,4,8,16. Open full size
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Four variants of this problem type
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
Audit a growth claim outside its graph window