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Math Help - I can't get the equation

  1. #1
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    Red face I can't get the equation

    An amoeba propogates by simple division: it takes 3 minutes for each split. We put such an amoeba in a glass container with nutriet fluid; it takes 1 hour unti the vessel is full of amobeas. How long will it take to fill the vessel, if we start not with 1 amoeba but 2?
    -Simulate data for 1 amoeba in a glass container until you can see a definate pattern.
    -Creat a function of time (call it f(t).) which will show the number of amoebas at anytime.
    -How many amoeba does it take to fill the glass conatiner?
    -Simulate data for starting with 2 amoeba in a glass container until you can see a difinite patter.
    -Create a function of time (call it g(t).) which will show the number of amoebas at anytime.
    -Use the function for starting with 2 amoeba and the knowledge of how many amoebas will fill the glass container to find out how long it takes to fill the glass conatiner when starting with 2 amoebas (NOTE: it takes longer than half an hour.)
    -show how to find the answer using data only
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  2. #2
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    -Simulate data for 1 amoeba in a glass container until you can see a definate pattern.
    (I cannot show a table form, so I will use [.......] as separators)

    t.............0,......1,......2,......3,......4,.. ....5,..

    minutes....0,......3,......6,......9,......12,.... .15,..

    amoebas...1,......2,......4,......8,......16,..... 32,..
    pattern....2^0,..2^1,..2^2,...2^3,..2^4,...2^5,..

    -----------------
    -Creat a function of time (call it f(t).) which will show the number of amoebas at anytime.

    f(t) = 2^t

    -------------
    -How many amoeba does it take to fill the glass conatiner?

    Since one t = 3minutes, then in one hour or 60 minutes, there are 60/3 = 20t
    That means after 20t, the container is full of amoebas.
    So, f(20) = 2^20 = 1,048,576 amoebas to fill the glass.

    --------------
    -Simulate data for starting with 2 amoeba in a glass container until you can see a difinite patter.

    t..............0,......1,......2,......3,......4,. .....5,..

    minutes.....0,......3,......6,......9,......12,... ..15,..

    amoebas....2,.....4,.......8,.....16,.....32,..
    pattern....2^1,..2^2,..2^3,...2^4,...2^5,..

    -------------
    -Create a function of time (call it g(t).) which will show the number of amoebas at anytime.

    g(t) = 2^(t+1)

    ----------
    -Use the function for starting with 2 amoeba and the knowledge of how many amoebas will fill the glass container to find out
    how long it takes to fill the glass conatiner when starting with 2 amoebas (NOTE: it takes longer than half an hour.)

    2^(t+1) = 1,048,576 = 2^20
    2^(t+1) = 2^20
    So,
    t+1 = 20
    t = 20 -1 = 19
    In minutes, that is 19(3) = 57 minutes

    --------------
    -show how to find the answer using data only

    Compare the two tables above.
    For 1 amoeba as starter, the number of amoebas at any time t is 2^t.
    For 2 amoebas as starter, the number of amoebas at any time t is 2^(t+1)
    That means the 2 amoebas are ahead by one t for the same number of propagated amoebas.
    Since one t is 3 minutes, and since 1 amoeba can fill up the container in 1 hour or in 60 minutes, then 2 amoebas can fill the container in 3 minutes before 1 hour....and that is 57 minutes.
    Last edited by ticbol; April 26th 2005 at 12:12 PM.
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  3. #3
    Site Founder Math Help's Avatar
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    How long will it take to fill the vessel, if we start not with 1 amoeba but 2?

    It should take 3 minutes less if you think about the fact that you are simply jumping to t=2 or 3minutes into the simulation when you start with 1 amoeba.
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  4. #4
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    Smile Thanks, I feel dumb now.........

    Thanks for the equation, I was making it way harder than it was suppose to be. We're getting into logs and lns so I was thinking about which equation to use, but none of them would work. My instructor is horrible, I think she did that on purpose!
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