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  • Perplex
    IB Math AIHL
    /
    Bivariate Statistics
    /

    Problem Bank

    [Maximum mark: 9]

    A reaction is studied in a school chemistry laboratory. The production rate ​R​ (​kg/h​) of a chemical is modeled as a cubic in the reactant concentration ​c​ (​mol/L​):

    ​
    R(c)=kc3+mc2+nc+p
    ​

    For four test runs, the technician recorded the concentration and the time to produce ​1kg​ of the chemical:

    Concentration ​c​ (​mol/L​)

    ​0.50​

    ​1.00​

    ​1.50​

    ​2.00​

    Time to produce ​1​ ​kg​ (​h/kg​)

    ​1.701​

    ​0.833​

    ​0.415​

    ​0.217​

    Using the table, one can compute the rate ​R​ (​kg/h​) at each concentration by inverting the “time per kg”.

    1. Use a cubic regression to determine ​k,m,n,​ and ​p​ and state the model.

      [3]

      To earn a crown, get your answer ready before you reveal the options!

    2. Using your model, estimate the time (in minutes) to produce ​1kg​ when ​c=1.80​ ​mol/L.

      [3]
    3. For what values of ​c​ in the range ​0.50≤c≤2.00​ does the model predict a rate of at least ​3.0​ ​kg/h?

      [3]

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