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Math Help - bacteria increase by 20%...

  1. #1
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    bacteria increase by 20%...

    A certain culture of bacteria intially contains 10,000 bacteria and increases by 20% every hour. Identify the explicit nth term of the sequence. how many bacteria are in the culture at the end of 10 hours? <-- thats basically exactly what the problem says. I could do it like hour per hour but there is probably a formula to solve these kinds of problems.. *it could come in handy too.
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  2. #2
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    Hello, arturju!

    A certain culture of bacteria intially contains 10,000 bacteria
    and increases by 20% every hour.
    Identify the explicit nth term of the sequence.
    How many bacteria are in the culture at the end of 10 hours?

    Let's baby-talk through this . . .

    There are X bacteria.

    At the end of an hour, there is 20% more bacteria, 0.20X more.
    . . So there is: .X + 0.20X .= .1.2X bacteria

    So the original amount in multiplied by 1.2 to give us the new amount.


    Since this happens every hour,
    . . at the end of two hours, there are: .(1.2)X bacteria
    . . and at the end of three hours, there are: .(1.2)X bacteria.


    The problem says that: X = 10,000
    Hence, at the end of n hours, there are: .10,000(1.2)^n bacteria

    At the end of 10 hours: .10,000(1.2)^10 . .61,917 bacteria.

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  3. #3
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    There is a very handy formula for expotential growth and decay: y=ce^(kt), where y is the new amount, c is the original, t is the time and k is a constant given by ln(f)/p where f is the factor of growth per time period p.
    y=(10000)e^(ln(1.2)*10) (ln(1.2) is divided by 1 here) I don't have a good calc around but I bet that gives you the right answer.
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