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Math Help - exponential growth problem

  1. #1
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    exponential growth problem

    I have totally forgotten how to do these questions, so I would really like to check my work...

    A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
    a) Find the doubling period.
    b) Determine the number of bacteria after 8 hours.

    what i did was...
    a) 12000 = 3000r^3
    and got r=1.59

    b) A=3000(1.59)^8
    =122545.7

    Is that right?
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  2. #2
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    Quote Originally Posted by bhuang View Post
    I have totally forgotten how to do these questions, so I would really like to check my work...

    A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
    a) Find the doubling period.
    b) Determine the number of bacteria after 8 hours.

    what i did was...
    a) 12000 = 3000r^3
    and got r=1.59

    b) A=3000(1.59)^8
    =122545.7

    Is that right?
    The working is good, didn't check your arithmetic
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  3. #3
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    Quote Originally Posted by bhuang View Post
    I have totally forgotten how to do these questions, so I would really like to check my work...

    A bacteria culture starts with 3000 bacteria and grows to a population of 12000 after 3 hours.
    a) Find the doubling period.
    b) Determine the number of bacteria after 8 hours.

    what i did was...
    a) 12000 = 3000r^3
    and got r=1.59
    That is r, but does not answer the question. Yes, 12000/3000= 4. 4 is 2 doubled and 2 is one doubled: the population has doubled twice in 3 hours. How long is each doubling period then?

    b) A=3000(1.59)^8
    =122545.7

    Is that right?
    (b) is approximately correct but notice that r^3= 4 so r is actually 4^{\frac{1}{3}} so the exact answer is 3000(4^{\frac{8}{3}}[/tex] which is (again approximately but, I think, more accurate) 120952.

    Once you have the correct answer to (a) you could also do that as 3000(2^{\frac{8}{T}} where "T" is the doubling time.
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