Unit 2: Functions
Topic 2.5: Exponential and Sinusoidal Models Questions
Practice 20 exam-style questions for IB Math AI SL Topic 2.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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A car''s value decays as V(t) = 18000 × (0.88)ᵗ. State the annual percentage decrease in value.
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A power model y = a·x² fits the data: when x = 4, y = 48.
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State the range of f(x) = 7 sin(2x) − 1.
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For y = 2 sin(πx) + 6, find the y-value when x = 0.5.
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A small village population of 800 grows by 4% per year.
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State whether the range of y = sin(x) is bounded or unbounded. Justify.
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For y = 4 sin(πx) + 1, write down the amplitude.
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A sinusoidal model has amplitude 4 and midline 3. State the maximum and minimum values.
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State whether f(t) = 1200 × (0.92)ᵗ represents growth or decay, and why.
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For the model f(t) = 800 × (1.05)ᵗ, write down the initial value.
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For y = 3 sin(x) + 5, state the maximum and minimum values.
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A printing service charges $20 plus $0.15 per page.
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A gym membership costs M(t) = 35t + 90, where t is months and M is dollars.
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The mass m of certain marbles is m = 5d³, where d is the diameter in cm and m is in grams. Find the mass of a marble with diameter 2 cm.
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For y = 6 cos(2x) − 3, write down the midline.
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A population grows as P(t) = 5000 × (1.03)ᵗ. State the annual percentage growth rate.
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A quantity decays as Q(t) = 200 × (0.5)ᵗ. Find Q(4).
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The number of users of an app is U(t) = 2000 × (1.4)ᵗ thousand, t in months. Find the number of users after 2 months.
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The height of the tide h metres at a harbour is modelled by h(t) = 3 sin(πt/6) + 5, where t is hours after midnight.
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