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Math Help - Calculus Word Problem

  1. #1
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    Calculus Word Problem

    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 65 cells. (The tolerance is 1% unless your instructor states otherwise.)

    (a) Find the relative growth rate.
    (b) Find an expression for the number of cells after t hours.
    (c) Find the number of cells after 6 hours.
    (d) Find the rate of growth after 6 hours.
    (e) When will the population reach 20,000 cells?


    My answers are :
    (a) k=

    (b) P(t)=

    (c) 17039360 billion cells

    (d)35432353 billion cells per hour

    (e) 2.75 hour

    According to the book only a and e are correct.

    Any help
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  2. #2
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    Quote Originally Posted by kashifzaidi View Post
    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 65 cells. (The tolerance is 1% unless your instructor states otherwise.)

    (a) Find the relative growth rate.
    (b) Find an expression for the number of cells after t hours.
    (c) Find the number of cells after 6 hours.
    (d) Find the rate of growth after 6 hours.
    (e) When will the population reach 20,000 cells?


    My answers are :
    (a) k=

    (b) P(t)=

    (c) 17039360 billion cells

    (d)35432353 billion cells per hour

    (e) 2.75 hour

    According to the book only a and e are correct.

    Any help

    Erasing those weird "billion" you wrote there, I find all the answers correct. Perhaps in part (b) it is writen p(t)=65\cdot 8^t , but this is exactly the same as what you wrote.

    Tonio
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