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IB Mathematics: Applications and Interpretation SL · 12.7: Mathematical Models · 12.7.3

Mixed modelling Problem set A Answers

Skills

    1. (a) k = 0.116
    2. (b) k = 0.0173
    3. (c) 0.756 years
    1. (a) A = 124, B = 16
    2. (b) k = 0.0903
    3. (c) 24.1 minutes
    1. (a) 29.5 mg
    2. (b) 15.0 hours
    1. (a) 2.19
    2. (b) For example: the rate of decrease stays proportional to the number present (nothing is added and the conditions do not change).
    3. (c) For large t the model gives a number between 0 and 1 fish (never 0), but a number of fish is a whole number and the fish would die out.

In context

    1. (a) p = 0.683, q = 2.05
    2. (b) R = 8.19
    3. (c) 74.6 ≤ A ≤ 322
    1. (a) p = 12.0
    2. (b) q = 2.00
    3. (c) 18.7 minutes
    1. (a) N = 6000e^(−0.173t)
    2. (b) After 50.2 years
    3. (c) The model never reaches 0 and gives fractions of an animal; in reality numbers are whole and chance matters when few are left.

Stretch

    1. (a) a = 2.00, b = 360 ÷ 24 = 15, c = 2.00, d = 7.00
    2. (b) Q = 1.00 sin(15(t − 5.00)) + 7.00
    1. (a) t = 0.0883
    2. (b) Maximum 16.8 at t = 8.98
    3. (c) Maximum (8.98, 16.8) and minimum (21.0, 11.2)
    4. (d) P + Q = 2.80 sin(15(t − 2.98)) + 14.0
    1. (a) 3800
    2. (b) A linear model grows without limit; a real population or market has a maximum size.
    3. (c) C = 1.50
    4. (d) k = 0.2
    5. (e) 4400

jmaths.xyz · AI SL · 12.7.3 Mixed modelling practice