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Math Help - logarhythms and exponential growth.

  1. #1
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    logarhythms and exponential growth.

    Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

    A bacteria divides every 20 minutes, so how many are there after 24 hours?

    Is this formula relevant here:
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  2. #2
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    Quote Originally Posted by lame_monkey View Post
    Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

    A bacteria divides every 20 minutes, so how many are there after 24 hours?

    Is this formula relevant here:
    No, does that even make sense?

    It divides every 20 minutes, so:

    N=N_0 2^{.05t}
    Last edited by colby2152; February 20th 2008 at 06:20 AM.
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  3. #3
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    colby there is no need for the constant term, it is just t in minutes over 20.
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  4. #4
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    Quote Originally Posted by lame_monkey View Post
    Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

    A bacteria divides every 20 minutes, so how many are there after 24 hours?

    Is this formula relevant here:
    Let t be measured in hours. So 20\  min = \frac13\ h

    If t = 0 you have N_0 bacteria.
    If t = 20\  min = \frac13\ h you have 2 \cdot N_0

    Now you can calculate the constant k:

    2 \cdot N_0 = N_0 \cdot e^{k \cdot \frac13}. Divide by N_0 and solve for k:

    2= e^{k \cdot \frac13}~\implies~\ln(2)=k \cdot \frac13~\implies~k=3\ln(2)

    And now plug in the time to calculate N_{24}:

    N_{24} = N_0 e^{3\ln(2) \cdot 24}~\approx~4.7224 \cdot 10^{21} \cdot N_0

    And that's a really big number.
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  5. #5
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    Thanks, that was really helpful.

    And I was able to follow it, which is always a good sign lol
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