Back to Topic 2.9 — HL modelling (HL only)
2.9.1Math AI HL8 flashcards

HL modelling — choosing & fitting a model

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Card 1 of 82.9.1
2.9.1
Question

How do you choose which function family to model a scenario with?

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All 8 Flashcards — HL modelling — choosing & fitting a model

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Card 1concept

Question

How do you choose which function family to model a scenario with?

Answer

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.

Card 2concept

Question

What is the key sign that a model should be logistic rather than exponential?

Answer

It grows fast at first but LEVELS OFF at a finite ceiling (carrying capacity). A plain exponential never flattens.

Card 3formula

Question

In y = L/(1 + C·e^{−kt}), what does L represent and how do you find it?

Answer

L is the carrying capacity (long-run ceiling): as t → ∞, e^{−kt} → 0 so y → L.

Card 4formula

Question

In y = L/(1 + C·e^{−kt}), what is the initial value (t = 0)?

Answer

Put t = 0: e⁰ = 1, so y(0) = L/(1 + C).

Card 5concept

Question

In N = k·e^{rt}, what do k and r mean?

Answer

k is the starting value (at t = 0); r is the continuous growth (r > 0) or decay (r < 0) rate.

Card 6formula

Question

In a sinusoidal model a·sin(b(t − c)) + d, what is each parameter?

Answer

a = amplitude (half the swing), d = midline (average level), period = 2π/b, c = horizontal shift.

Card 7concept

Question

How do you write a bulk-discount cost as a piecewise function?

Answer

One linear rule up to the threshold, then a second linear rule (fixed cost so far + new lower rate × extra units) beyond it.

Card 8concept

Question

After fitting a model, what should you always do for the marks?

Answer

Interpret each parameter in context AND comment on validity (where the model is reliable vs where extrapolation is unsafe).

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IB Math AI HL modelling — choosing & fitting a model Flashcards | 2.9.1 | Aimnova | Aimnova