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F-LE.3 Core M2-026-R10-V03

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

Audit a growth claim outside its graph window

Problem

Audit extrapolation from the near agreement on \(0\le~t\le~5\). Calculate \(\text{both}~\text{models}\) at \(t=5\) and \(t=25\), compare their long-run values, and flag the contextual issue created when the linear model becomes negative.

Source graph of L(t)=100−5t and E(t)=100(0.95)^t on 0≤t≤5, with L(5)=75 and E(5)≈77.38. 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