Results 1 to 3 of 3

Math Help - Amoeba doubles every 2.5 days.

  1. #1
    Newbie
    Joined
    Feb 2014
    From
    New York
    Posts
    16

    Amoeba doubles every 2.5 days.

    I was wondering how to set up an equation for this. A single cell double every 2.5 days. How many days will it take 1 amoeba to produce 10,000? Thank you for the help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,004
    Thanks
    1660

    Re: Amoeba doubles every 2.5 days.

    "Doubling" goes 2, 4= 2^2, 2(4)= 8= 2^3, etc. In other words, doubling n times gives 2^n so you need to solve 2^n= 10000.
    That is an "exponential" problem so take the logarithm of both sides. log(2^n)= n log(2)= log(10000) and then n= \frac{log(10000)}{log(2)}.

    That is the "number of doublings" and since each doubling requires 2.4 days, divide that by 2.4 to get the number of days.

    You could also do that just by continuing: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 which is larger than 10000, but that won't give you the fraction between 13 and 14 doublings.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,803
    Thanks
    1692
    Awards
    1

    Re: Amoeba doubles every 2.5 days.

    Quote Originally Posted by HallsofIvy View Post
    "Doubling" goes 2, $4= 2^2$, $2(4)= 8= 2^3$, etc. In other words, doubling n times gives $2^n$ so you need to solve $2^n= 10000$.
    That is an "exponential" problem so take the logarithm of both sides. $log(2^n)= n log(2)= log(10000)$ and then $n= \dfrac{log(10000)}{log(2)}$.

    That is the "number of doublings" and since each doubling requires 2.4 days, divide that by 2.4 to get the number of days.

    You could also do that just by continuing: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 which is larger than 10000, but that won't give you the fraction between 13 and 14 doublings.
    TeX fixed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pre-calc amoeba doubling every 4 days
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 3rd 2013, 03:17 PM
  2. Replies: 8
    Last Post: February 11th 2011, 08:59 AM
  3. [SOLVED] Calculating When A Number Doubles
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 10th 2009, 03:20 AM
  4. Dice and Doubles
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 12th 2008, 03:21 PM
  5. Amoeba-doubling problem, help please
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 10th 2006, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum