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M1-032-A04-V03
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F-LE.3
Warmup
M1-032-A04-V03
Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Compare quadratic and exponential graphs using long-term behavior
Problem
Analyze the displayed graph to estimate both intersections of \(Q\) and \(E\), compare the models before, between, and after them within the window, and state the precision and scope of the graph evidence.
Answer choices
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A
visible comparisons = Q>E before c₁ and after c₂; E>Q between; equality = E=Q at c₁,c₂; estimate status = graph estimates are exact; scope = all real inputs are established
B
visible comparisons = E>Q between the intersections and Q>E outside; equality = E=Q at c₁,c₂; estimate status = estimates are exact; scope = all real inputs follow the same pattern
C
visible comparisons = E>Q outside and Q>E between the intersections; equality = E=Q at c₁,c₂; estimate status = estimates prove exact algebraic values; scope = no further data are needed
D
visible comparisons = E>Q for x<c₁ and x>c₂ within window; Q>E for c₁<x<c₂; equality = E=Q at c₁,c₂; estimate status = c₁,c₂ are graph estimates unless coordinates or formulas are given; scope = no claim outside displayed window
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Curriculum context
Standard F-LE.3
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Problem type Compare quadratic and exponential graphs using long-term behavior
