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    Isolating T value

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    The probability R called risk that an exceedance occurs at least once in n successive years.
    R = 1 - (1-1/T)^n
    T= Return period
    EXAMPLE: What return period must a hydrologist use in designing a critical spillway to accept only a 10% risk that flooding will occur in the next 5 years?
    0.10 = 1 - (1-1/T)^5
    T=48.1 years
    HOW? Show me the steps to isolate T

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    Solution Preview


    Normally, the best way to isolate a variable where powers are involved is to use logs.

    1)0.10 = 1 - (1-1/T)^5
    0.10 - 1 = -(1-1/T)^5
    -0.9 = -(1-1/T)^5

    2)Multiply both sides ...

    Solution Summary

    Detailed help in isolating t-value in a given equation is provided.