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Math Help - expoenential

  1. #1
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    expoenential

    20 The number of parts per million, x, of E. coli in a stream t hours after a pollutant
    containing E. coli is introduced is modelled by x(t) = loge (t + e^2), t ≥ 0.
    a How many parts per million of E. coli are introduced into the stream?
    b To the nearest tenth of a part per million, how many parts per million of E. coli are in the stream when t = 10?


    could some one help me with part b?
    i tried subin t=10
    therefore i got x(10)= loge ( 10 + e^2)
    = loge 10 * loge e^2
    = 4.605
    but the answer is wrong.
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  2. #2
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    Quote Originally Posted by rachael
    20 The number of parts per million, x, of E. coli in a stream t hours after a pollutant
    containing E. coli is introduced is modelled by x(t) = loge (t + e^2), t ≥ 0.
    a How many parts per million of E. coli are introduced into the stream?
    b To the nearest tenth of a part per million, how many parts per million of E. coli are in the stream when t = 10?

    could some one help me with part b?
    i tried subin t=10
    therefore i got x(10)= loge ( 10 + e^2)
    = loge 10 * loge e^2
    = 4.605
    but the answer is wrong.
    Hello,

    you only have to plug in the values you know into the given equation:
    x(t) = log_{e} (t + e^2). If t = 10, you'll get:
    x(t) = log_{e} (10 + e^2)\approx 2.8558...

    (By the way: You are right: The logarithm of a product is a sum, but the logarithm of a sum is not a product.)

    (For log_{e} you better use ln and then you'll find the correct button on your calculator more easily.)

    Greetings

    EB
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