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Math Help - Exponential Function

  1. #1
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    Exponential Function

    A statistical study indicates that the fraction of the electric toasters manufactured by a certain company that are still in working condition after t years of use is approximately  f(t) = e^{-0.2t}.

    a) What fraction of the toasters can be expected to fail before one year of use?
    b) What fraction of the toasters can be expected to fail during the third year of use?
    I'm not sure how to solve this question without knowing the equation for failure of use in t... please help me?

    Here are the textbook answers...
    a) 0.1812
    b) 0.1215
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Macleef View Post
    I'm not sure how to solve this question without knowing the equation for failure of use in t... please help me?

    Here are the textbook answers...
    a) 0.1812
    b) 0.1215
    please don't put your questions between quote tags, they are not quoted automatically when someone responds to your post.


    now, the formula given gives the fraction for those still working, hence, the fraction for those not working is given by: 1 - (fraction of those still working)
    A statistical study indicates that the fraction of the electric toasters manufactured by a certain company that are still in working condition after t years of use is approximately .

    a) What fraction of the toasters can be expected to fail before one year of use?
    this is 1 - f(1) = what the text says, well, the last 2 should be 3

    b) What fraction of the toasters can be expected to fail during the third year of use?
    after 2 years, f(2) still worked. after 3 years, f(3) still worked.

    thus the amount that failed during the 3rd year is f(2) - f(3) = what the text says
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  3. #3
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    Quote Originally Posted by Macleef View Post
    A statistical study indicates that the fraction of the electric toasters manufactured by a certain company that are still in working condition after t years of use is approximately .

    a) What fraction of the toasters can be expected to fail before one year of use?
    b) What fraction of the toasters can be expected to fail during the third year of use?
    fraction to fail before one year = f(0) - f(1) = .1813

    fraction expected to fail during the third year = f(2) - f(3) = .1215
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