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IB Mathematics: Applications and Interpretation HL · 12.7: Mathematical Models · 12.7.1

Linear, quadratic, cubic, variation and exponential models Problem set A Answers

Skills

    1. (a) \(C=3d+5\)
    2. (b) £27.50
    1. (a) x = 14, P = 228
    2. (b) x = 5.28 and x = 22.7
    1. (a) \(0<x<12\)
    2. (b) 1620 cm³
    3. (c) 1830 cm³ (x = 4.71)
    1. (a) a = 0.06
    2. (b) 54 m
    1. (a) y = 12
    2. (b) 42
    3. (c) x = 5.92

In context

    1. (a) \(V=10t+40\)
    2. (b) 21 minutes
    3. (c) \(0\le t\le26\)
    1. (a) 40 m
    2. (b) 16 m
    3. (c) 20 m
    1. (a) 0.7276
    2. (b) 82.7%
    3. (c) 8.91 hours
    1. (a) k = 42
    2. (b) 6 hours
    3. (c) 11

Stretch

    1. (a) t = 8, N = 128
    2. (b) 5.58 ≤ t ≤ 10, 4.42 hours
    3. (c) N is negative after t = 12
    1. (a) \(T=95-3.3t\)
    2. (b) −37 °C. Below the room temperature of 25 °C, which is impossible.
    3. (c) 25.3 °C
    4. (d) The exponential model. It levels off just above the room temperature, as the data does. The linear model keeps falling at a constant rate, so it goes below the room temperature.

jmaths.xyz · AI HL · 12.7.1 Linear, quadratic, cubic, variation and exponential models