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IB Mathematics: Applications and Interpretation HL · AHL 8: Statistics 2 · AHL 8.3

Paper 3 modelling: a logistic model Problem set A Answers

Fit the model

    1. (a) 1250 thousand users is the maximum number of active users the app will have (the carrying capacity). N gets closer to 1250 as t increases, but never reaches it.
    2. (b) \(C=24e^{2k}\)
    3. (c) \(C=4e^{7k}\)
    1. (a) k = 0.358
    2. (b) C = 49.1

Judge the model

    1. (a) a = 136.0
    2. (b) \(SS_{res}\) = 1.59
    1. (a) E = 0.630 < 0.8, so the model will be used

Use the model

    1. (a) 1160 thousand users
    2. (b) \(R=\dfrac{750}{1+49.1e^{-0.358t}}\)
    1. (a) 20 agents per year
    2. (b) t = 7.40, in the year 2027

jmaths.xyz · AI HL · AHL 8.3 Paper 3 modelling: a logistic investigation