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IB Mathematics: Applications and Interpretation HL · 12.7: Mathematical Models · 12.7.4

Sinusoidal and logistic models Problem set A Answers

Skills

    1. (a) \(P=4\sin(0.419(t-2))+10\)
    2. (b) P = 13.8
    1. (a) \(P=11\sin(0.524(t-3))+20\)
    2. (b) P = 29.5
    1. (a) \(P=6\sin(0.785(t-1.5))+20\)
    2. (b) P = 25.5
    1. (a) C = 19
    2. (b) k = 0.643
    1. (a) P = 464
    2. (b) t = 7.40

In context

    1. (a) \(D=1.4\sin(0.507(t-1.1))+3.2\)
    2. (b) 4.49 m
    1. (a) \(T=12\sin(0.262(t-9))+26\)
    2. (b) 34.5 °C
    1. (a) C = 39, k = 0.352
    2. (b) 601 bacteria
    1. (a) \(h=0.35\sin(2.09(x-0.5))+1.2\)
    2. (b) 1.41 m

Stretch

    1. (a) L = 600
    2. (b) P(0) = 30
    3. (c) t = 5.89, P = 300
    4. (d) The logistic curve levels off at 600. The exponential curve keeps rising without limit.
    1. (a) t = 2.30
    2. (b) t = 6.10

jmaths.xyz · AI HL · 12.7.4 Sinusoidal and logistic models