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  • Perplex
    IB Math AISL
    /
    Exponents & Logarithms
    /

    Problem Bank

    [Maximum mark: 16]

    After cooking a large batch of chili, James puts it immediately in the fridge. The temperature ​T, in ​∘C, ​t​ hours after it is placed in the fridge is given by ​T(t)=90e−5t/M+2, where ​M​ is the mass in kilograms of the chili.

    1. Write down

      1. the initial temperature of the chili;

        [2]

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

      2. the temperature of the fridge.

        [2]

    Consider the equation ​T(t)=k.

    1. Show that time taken for the chili to reach a temperature of ​k°C​ is given by ​t=−5M​ln(90k−2​).

      [3]

    Food safety rules dictate that food should not sit in the "danger zone" of ​4°Cto56∘C​ for more than two hours.


    James calculates that the time his batch of chili will spend in the danger zone is ​aM, where ​a∈R.

    1. Using the result from (b), find the value of ​a.

      [5]
    2. Hence, determine the largest batch of chili James can safely store in his fridge.

      [3]
    3. Suggest one way James could store a larger batch safely.

      [1]

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