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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 B Answers

Skills

    1. (a) \(C=26d+18\)
    2. (b) £174.00
    1. (a) x = 13, P = 98
    2. (b) x = 6 and x = 20
    1. (a) \(0<x<15\)
    2. (b) 3696 cm³
    3. (c) 4100 cm³ (x = 6.07)
    1. (a) a = 0.25
    2. (b) 250 kW
    1. (a) y = 5
    2. (b) 29
    3. (c) x = 6.04

In context

    1. (a) \(V=12t+18\)
    2. (b) 8.5 minutes
    3. (c) \(0\le t\le11\)
    1. (a) 30 m
    2. (b) 11.25 m
    3. (c) 16.1 m
    1. (a) 0.7784
    2. (b) 27.4 °C
    3. (c) 11.9 minutes
    1. (a) k = 90
    2. (b) 15 days
    3. (c) 12

Stretch

    1. (a) t = 6, V = 108
    2. (b) 4 ≤ t ≤ 7.62, 3.62 weeks
    3. (c) V is negative after t = 9
    1. (a) \(T=90-3.4t\)
    2. (b) −46 °C. Below the room temperature of 18 °C, which is impossible.
    3. (c) 18.3 °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