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Math Help - E.Coli exponential growth problem, what am i doing wrong?

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    Unhappy E.Coli exponential growth problem, what am i doing wrong?

    E.Coli exponential growth problem, what am i doing wrong?
    Okay, so I have found the correct formula for this problem, but for some reason I must be doing something wrong, because I can't get the right answer. Here is the Original Problem, and I will go through what I did:

    A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells.
    a) find relative growth rate. k= 2.08 (thats right)
    b) Find an expression for the number of cells after t hours. = P(t)=55e^(2.08t) (this is right)

    now, for c) it asks: Find the number of cells after 5 hours
    ________ billion cells. however, the number I am getting by just plugging it into the calculator, is 1807279.412. So i divided it by 1000, and said that it is 1807.279 billion. But Is this wrong?

    Also, how do I find the rate of growth after 5 hours?

    I feel like I must be doing something kind of stupid, because it seems smile enough. Thanks!
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  2. #2
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    Quote Originally Posted by keeg View Post
    E.Coli exponential growth problem, what am i doing wrong?
    Okay, so I have found the correct formula for this problem, but for some reason I must be doing something wrong, because I can't get the right answer. Here is the Original Problem, and I will go through what I did:

    A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells.
    a) find relative growth rate. k= 2.08 (thats right)
    b) Find an expression for the number of cells after t hours. = P(t)=55e^(2.08t) (this is right)

    now, for c) it asks: Find the number of cells after 5 hours
    ________ billion cells. however, the number I am getting by just plugging it into the calculator, is 1807279.412. So i divided it by 1000, and said that it is 1807.279 billion. But Is this wrong?

    Also, how do I find the rate of growth after 5 hours?

    I feel like I must be doing something kind of stupid, because it seems smile enough. Thanks!
    ... are you sure the initial population was just 55 cells?
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    Yeah, its only 55 cells. here is the question verbatim:
    A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells. (The tolerance is 1% unless your instructor states otherwise.)
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    Quote Originally Posted by keeg View Post
    Yeah, its only 55 cells. here is the question verbatim:
    A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells. (The tolerance is 1% unless your instructor states otherwise.)
    k = \ln(8)

    P(t) = 55e^{kt}

    P(5) = 55e^{5k} = 1802240 cells

    number of cells in billions ... (note that a billion is 10^9)

    P(5) = \frac{1802240}{10^9} = 1.8 \times 10^{-3} billion cells

    rate of growth is \frac{dP}{dt} = kP ...

    at t = 5 hrs, \frac{dP}{dt} = 3.7 \times 10^6 bacteria/hr
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