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M1-032-A01-V02
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F-LE.3
Warmup
M1-032-A01-V02
Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Compare linear and exponential values over the same inputs
Problem
Use the displayed table to determine the linear and exponential models, compare their values at every listed input, and locate the crossing bracket and first listed integer where the exponential model overtakes the linear model.
Answer choices
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A
models = L(x)=5+10x and E(x)=2·3ˣ; comparisons = L>E at x=0,1; E>L at x=2,3,4; crossing bracket = between x=1 and x=2; first listed integer overtake = x=2 because exponentials eventually win
B
models = L(x)=5+10x and E(x)=2·3ˣ; comparisons = L>E at x=0,1,2; E>L at x=3,4; crossing bracket = between x=2 where 25>18 and x=3 where 54>35; first listed integer overtake = x=3
C
models = L(x)=5+10x and E(x)=2·3ˣ; comparisons = L>E at x=0,1,2; E>L at x=3,4; crossing bracket = between x=2 where 25>18 and x=3 where 54>35; first listed integer overtake = x=4 because it is the fourth value after x=0
D
models = L(x)=10x+5 and E(x)=3·2ˣ; comparisons = L>E at x=0,1,2; E>L at x=3,4; crossing bracket = between x=2 and x=3; first listed integer overtake = x=3
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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 linear and exponential values over the same inputs
