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

Sinusoidal and logistic models Problem set B Answers

Skills

    1. (a) \(P=7\sin(0.314(t-3))+25\)
    2. (b) P = 32
    1. (a) \(P=18\sin(0.785(t-1))+30\)
    2. (b) P = 46.6
    1. (a) \(P=15\sin(0.628(t-2))+55\)
    2. (b) P = 67.1
    1. (a) C = 24
    2. (b) k = 0.534
    1. (a) P = 352
    2. (b) t = 3.39

In context

    1. (a) \(h=0.17\sin(7.85(t-0.1))+0.45\)
    2. (b) 0.607 m
    1. (a) \(E=12\sin(0.262(t-6))+40\)
    2. (b) 50.4 GW
    1. (a) C = 39, k = 0.422
    2. (b) 293 fish
    1. (a) \(h=0.12\sin(6.98(x-0.1))+1.5\)
    2. (b) 1.60 m

Stretch

    1. (a) L = 400
    2. (b) P(0) = 50
    3. (c) t = 2.43, P = 200
    4. (d) The logistic curve levels off at 400. The exponential curve keeps rising without limit.
    1. (a) t = 3.47
    2. (b) t = 10.5

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