Results 1 to 2 of 2

Math Help - Doubling time!

  1. #1
    Member
    Joined
    Nov 2007
    Posts
    112

    Doubling time!

    If the size of a bacteria colony doubles in 6 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

    Exact:

    Decimal (nearest hundreth):


    ok so i know the equation that i have to use, i believe its,

    2=(1+r/100)^t

    and then for the tripleing time you just find, r, and plug it in...can someone let me know if im on the right track..thanks

    mathlete
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by mathlete View Post
    If the size of a bacteria colony doubles in 6 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.
    ...
    Hi,

    1. I assume exponential growth
    2. let a be the initial amount of bacteria

    With exponential growth you use the equation:

    A(t) = A(0) \cdot e^{k \cdot t} with A(t) = amount at the time t, and A(0) = initial value.

    From your problem you know: A(6) = 2a

    2a = a \cdot e^{k \cdot 6}~\iff~2 = e^{k \cdot 6} ~\iff~ \ln(2)= k\cdot 6~\iff~ k= \frac16 \cdot \ln(2)

    Use these results to calculate A(t) = 3a

    3a = a \cdot e^{\frac16 \cdot \ln(2) \cdot t}~\iff~3 = e^{\frac16 \cdot \ln(2) \cdot t} ~\iff~ \ln(3)= \frac16 \cdot \ln(2) \cdot t ~\iff~ t= 6 \cdot \frac{\ln(3)}{\ln(2)}

    Use a calculator to get the approximative value of t \approx 9.50977... \approx 9.51
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help finding the doubling time
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 17th 2010, 04:01 PM
  2. doubling time
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 16th 2009, 08:20 AM
  3. Doubling time
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 2nd 2009, 06:37 PM
  4. doubling time
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 26th 2009, 10:46 PM
  5. Doubling Time from population growth equation
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: September 30th 2007, 12:42 PM

Search Tags


/mathhelpforum @mathhelpforum