Results 1 to 2 of 2

Math Help - Exponential/Log Function help

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    50

    Exponential/Log Function help

    I Can't seem to figure out how to show the work for this question

    For a biology experiment, there are 50 cells present. After 2 hours there are 1600 bacteria. How many bacteria would there be after 6 hours?

    The answer is 1 638 400 but I don't know how to get to that answer. Can someone help me out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by Hockey_Guy14 View Post
    I Can't seem to figure out how to show the work for this question

    For a biology experiment, there are 50 cells present. After 2 hours there are 1600 bacteria. How many bacteria would there be after 6 hours?

    The answer is 1 638 400 but I don't know how to get to that answer. Can someone help me out?
    Hello,

    we assume exponential growth.
    The amount of bacteria with respect to time can be calculated by:

    a(t) = a(0) \cdot e^{k\cdot t}.......... Thus you have to calculate the constants a(0) and k from the given conditions:

    t = 0 and a(0) = 50

    t = 2 and a(2) = 1600. Therefore:

    1600 = 50 \cdot e^{k \cdot 2}

    32 = e^{k \cdot 2}

    \ln(32) = k \cdot 2 ~\implies~ k = \frac12 \cdot \ln(32)

    Now you can calculate a(6):

    a(6)= 50 \cdot e^{\frac12 \cdot \ln(32) \cdot 6}=50 \cdot 32^3= 1,638,400
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: April 17th 2012, 10:50 AM
  2. Replies: 11
    Last Post: May 9th 2010, 08:55 AM
  3. Replies: 0
    Last Post: August 31st 2009, 02:02 AM
  4. Replies: 2
    Last Post: March 30th 2008, 02:28 PM
  5. Replies: 3
    Last Post: July 17th 2007, 11:06 AM

Search Tags


/mathhelpforum @mathhelpforum