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  • Perplex
    IB Math AAHL
    /
    Approximations & Error
    /

    Problem Bank

    [Maximum mark: 7]

    The rate of heat production of bears is proportional to the cube of its height, measured from foot to shoulder.

    1. A black bear with height ​70cm​ produces heat at a rate of ​250W.

      1. Find an expression for the rate of energy consumption of a bear in terms of its shoulder height, ​h, in meters.

        [3]

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

      2. Hence find the rate of heat production of a ​120cm​ brown bear. Give your answer to the nearest ​100W.

        [2]

    In the arctic, the rate of heat loss, in Watts, is given by ​800h2.

    1. Find the minimum shoulder height for a polar bear to survive the arctic cold.

      [2]

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