Results 1 to 2 of 2

Math Help - Logarithmic Modeling problem

  1. #1
    Senior Member
    Joined
    Jul 2007
    Posts
    290

    Logarithmic Modeling problem

    Ok I've been quite stuck on this for a little while and as always, I have the worst time setting up the problem.


    An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take for the the critical level to be reached if the same person is infected with 10 bacteria?


    I know we use the exponential growth formula but i'm uncertain as to how to set it up with the problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by JonathanEyoon View Post
    Ok I've been quite stuck on this for a little while and as always, I have the worst time setting up the problem.


    An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take for the the critical level to be reached if the same person is infected with 10 bacteria?


    I know we use the exponential growth formula but i'm uncertain as to how to set it up with the problem.
    The number doubles in 1 hour, so N=2^t, where t is measured in hours from
    infection.

    To grow to 10 it would take:

    t = log_2(10) hours

    Therefore they will fall ill 24-log_2(10) = 24-3.32 = 20.68 hours after infection with 10 bacteria.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Exponential modeling problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 30th 2011, 03:45 AM
  2. Can't figure out how to set up this modeling problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 28th 2011, 07:50 PM
  3. Modeling the following problem as a PDE
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 19th 2010, 05:17 PM
  4. A problem on ODE modeling
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: January 7th 2010, 02:38 AM
  5. Modeling Problem
    Posted in the Calculus Forum
    Replies: 27
    Last Post: May 3rd 2009, 04:47 PM

Search Tags


/mathhelpforum @mathhelpforum