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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 Summary

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

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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 ...

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