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How do you choose which function family to model a scenario with?
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All Flashcards in Topic 2.9
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2.9.18 cards
How do you choose which function family to model a scenario with?
Match the behaviour: steady change → linear; one peak → quadratic; constant multiplier each step → exponential; fast-then-levels-off at a ceiling → logistic; repeats/oscillates → sinusoidal; different rule on each interval → piecewise.
What is the key sign that a model should be logistic rather than exponential?
It grows fast at first but LEVELS OFF at a finite ceiling (carrying capacity). A plain exponential never flattens.
In y = L/(1 + C·e^{−kt}), what does L represent and how do you find it?
L is the carrying capacity (long-run ceiling): as t → ∞, e^{−kt} → 0 so y → L.
In y = L/(1 + C·e^{−kt}), what is the initial value (t = 0)?
Put t = 0: e⁰ = 1, so y(0) = L/(1 + C).
In N = k·e^{rt}, what do k and r mean?
k is the starting value (at t = 0); r is the continuous growth (r > 0) or decay (r < 0) rate.
In a sinusoidal model a·sin(b(t − c)) + d, what is each parameter?
a = amplitude (half the swing), d = midline (average level), period = 2π/b, c = horizontal shift.
How do you write a bulk-discount cost as a piecewise function?
One linear rule up to the threshold, then a second linear rule (fixed cost so far + new lower rate × extra units) beyond it.
After fitting a model, what should you always do for the marks?
Interpret each parameter in context AND comment on validity (where the model is reliable vs where extrapolation is unsafe).
Topic 2.9 study notes
Full notes & explanations for HL modelling (HL only)
Math AI exam skills
Paper structures, command terms & tips
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