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F-LE.3 Core M2-026-R10-V04

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

Audit a growth claim outside its graph window

Problem

Audit a claim that the ordering at \(t=6\) persists forever. Calculate \(\text{both}~\text{models}\) at \(t=6\) and again at \(t=20\), compare the pairs, and explain how the displayed window can miss a later exponential crossover.

Source graph of P(t)=10t³ and E(t)=100(1.4)^t on 0≤t≤6, ending with P(6)=2160 and E(6)≈752.95. 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