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  • Perplex
    IB Math AAHL
    /
    Approximations & Error
    /

    Problem Bank

    [Maximum mark: 6]

    The magnitude ​M​ of an earthquake on the Richter scale is defined as a function of the energy, in joules, ​E​ released by the earthquake:

    ​
    M=32​logE−516​.
    ​

    Using this equation, it can be shown that

    ​
    E=a×10bM.
    ​
    1. Find the value of ​a​ and the value of ​b.

      [3]

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

    On July ​22, ​2023, Taylor Swift fans in Seattle registered a ​2.3​ magnitude earthquake. The largest earthquake ever recorded, the ​1960​ Valdivia earthquake off the coast of Chile, had a ​9.5​ magnitude.

    1. Find the number of "Swift Quakes" needed to match of energy of the Valdivia earthquake. Give your answer in the form ​c×10k, where ​1≤c<10​ and ​k∈Z.

      [3]

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