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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 B Answers

Fit the model

    1. (a) 64 thousand members is the maximum number of members the scheme will have (the carrying capacity). N gets closer to 64 as t increases, but never reaches it.
    2. (b) \(C=15e^{2k}\)
    3. (c) \(C=0.6e^{7k}\)
    1. (a) k = 0.644
    2. (b) C = 54.4

Judge the model

    1. (a) a = 20.2
    2. (b) \(SS_{res}\) = 0.35
    1. (a) E = 0.296 < 0.35, so the model will be used

Use the model

    1. (a) 63.9 thousand members
    2. (b) \(R=\dfrac{2816}{1+54.4e^{-0.644t}}\)
    1. (a) 300 bikes per year
    2. (b) t = 6.56, in the year 2025

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