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F-LE.3 Warmup M2-026-A07-V03

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

Select a usable window around a computed crossover

Problem

Compute \(\text{both}~\text{models}\) at \(t=20\) and \(t=21\) to bracket the first integer overtake, retaining enough precision for the comparison. Evaluate each window for inclusion of \(\text{both}~\text{adjacent}~\text{inputs}\) and \(\text{all}~\text{four}~\text{values}\), then use the \(350\text{-}\text{pixel}\) height to reject an unnecessarily broad scale.

Source graphic for L(t)=1000+5t and E(t)=900(1.01)^t with candidate windows W1=[0,10]×[850,1100], W2=[0,25]×[850,1200], W3=[0,500]×[0,130000], and W4=[20,25]×[0,100]. 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
Select a usable window around a computed crossover