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M1-032-A08-V02
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F-LE.3
Warmup
M1-032-A08-V02
Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Interpret an overtaking point in context
Problem
Interpret the overtaking point of \(L\) and \(E\) in the displayed context graph. State the approximate equality and difference at the crossing, compare the models before and after it, and report the estimate status with the contextual units.
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A
at overtake = L(10)≈E(10); before = E>L before 10; after = L>E after 10; status = estimated; units = months and people
B
at overtake = L(10)≈E(10); before = L>E before 10; after = E>L after 10; status = equality is proven for every nearby time; units = months and people
C
at overtake = L(10)=E(10)=10 people; before = L>E before 10; after = E>L after 10; status = exact from the label; units = months and people
D
at overtake = L(10)≈E(10) people and E-L≈0; before = L(t)>E(t) for modeled months before about 10; after = E(t)>L(t) for modeled months after about 10; status = month 10 is an estimate unless exact equations verify it; units = months and people
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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 Interpret an overtaking point in context