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  • Perplex
    IB Math AIHL
    /
    Bivariate Statistics
    /

    Problem Bank

    [Maximum mark: 8]

    Denise brews a cup of coffee and leaves it in a room at a constant ​20°C. She uses a temperature probe to record the coffee’s temperature every ​4​ minutes, obtaining the following data:

    Time ​t​ (min)

    0

    4

    8

    12

    16

    20

    24

    Temperature ​T​ (°C)

    85

    68

    56

    47

    41

    36

    33

    After graphing the data, Denise believes a suitable model will be ​T=20+abt,a,b∈R.

    1. Explain why ​T−20​ can be modeled by an exponential function.

      [1]
    2. Find the equation of the least squares exponential regression curve for ​T−20.

      [3]
    3. Write down the coefficient of determination, ​R2.

      [1]
    4. Interpret what the value of ​R2​ implies about the model.

      [1]
    5. Hence predict the temperature of the coffee after ​14​ minutes.

      [2]

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