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M1-032-A08-V03
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F-LE.3
Warmup
M1-032-A08-V03
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 \(S\) and \(F\) in the displayed context graph. State the approximate equality and difference at the crossing, compare the models before and after it, and explain the estimate status for whole-week data with the contextual units.
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A
at overtake = S(8)≈F(8) users and F-S≈0; before = S(w)>F(w) for modeled weeks before about 8; after = F(w)>S(w) for modeled weeks after about 8; status = week 8 is an approximate crossing, and whole-week data may bracket rather than contain exact equality; units = weeks and users
B
at overtake = S(8)≈F(8); before = F>S before 8; after = S>F after 8; status = approximate; units = weeks and users
C
at overtake = S(8)≈F(8); before = S>F before 8; after = F>S after 8; status = whole-week inputs guarantee exact equality; units = weeks and users
D
at overtake = S(8)=F(8)=8 users; before = S>F before 8; after = F>S after 8; status = exact at the whole-week input; units = weeks and users
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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