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Math Help - Algebraic Methods

  1. #1
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    Algebraic Methods

    Been trying to solve this for days please please help. Probably something simple im missing.

    'The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula

    x = 3 + ln(y/1-y)

    Determine the probability of breakdown for 1, 3 and 10years.
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by gav1981 View Post
    Been trying to solve this for days please please help. Probably something simple im missing.

    'The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula

    x = 3 + ln(y/1-y)

    Determine the probability of breakdown for 1, 3 and 10years.
    You want to isolate y in this equation...

    e^{x-3}=\frac{y}{1-y}

    e^{x-3}-ye^{x-3}=y

    e^{x-3}=y(e^{x-3}+1)

    y=\frac{e^{x-3}}{e^{x-3}+1} \Rightarrow \frac{1}{1+e^{3-x}}

    Now, plug and chug for values of x.
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