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Math Help - Help with floor function involving bacteria?

  1. #1
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    Help with floor function involving bacteria?

    I know how to figure this question out if there is a ending amount of hours (such as how many bacteria will be there at the end of 8 hours), but when there is a floor function thrown in there I have no clue how to solve this or where to start. Any help would be appreciated.

    The floor function denoted [x], outputs the greatest integer less than or equal to x. So, [7.3]=7, [27]=27, and [-3.5]=-4. A certain strain of bacteria that is growing on your kitchen counter doubles every 5 minutes. Assume that you start with only one bacterium.

    a) What quantities are changing in this situation? What quantities are not changing?
    b) Use the floor function to define a function that gives the number of bacteria present after t minutes.
    c) Represent the number of bacteria present after 30 minutes? How many bacteria are there?
    d) How many bacteria are present after 2 minutes? 5 minutes? 14.75 minutes? 23.22 minutes? 47.92 minutes?
    e) Determine the approximate number of minutes for the number of bacteria to reach 2000.
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  2. #2
    Newbie driegert's Avatar
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    Feb 2010
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    Kingston, Ontario
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    Hey,

    a) so the quantities that are changing should be the time, and the number of bacteria.
    b) This is really similar to compound interest or half-life questions.. I'm thinking something like

     B(t) = [(2^{t/5}) x_{0}] where B(t) would be the number of bacteria at minute t. and x_{0} is the starting number of bacteria (in our case, 1). So we can see that in 5 minutes, we'll have 2 bacteria, 10 minutes we'll have 4, etc.

    The rest of the questions involve using this formula (if it's right... I think it is).

    Hope that helps! (Hope you learned from it too!)
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