Results 1 to 2 of 2

Thread: Exponential Growth & Decay

  1. #1
    Member realintegerz's Avatar
    Joined
    Aug 2008
    Posts
    109

    Exponential Growth & Decay

    Hi, I'm reviewing for a test that will happen this week and I need some help on these problems..

    1) A yeast colony is growing exponentially, it starts with 300 individuals and 4 hours later it has 5000 individuals.

    A) How long will it take to have 20,000 individuals?
    b) What is the doubling time for this colony?

    2) A radioactive substance has a half life of 8,000 years, how long does it take to lose 1% of the substance to radioactive decay?


    In these problems, I'm just not getting how to figure out the time with the initial amount known and multiplying factor known... I tried doing some calculating but they aren't coming out right

    I can do problems like these where the time is given but I have not been taught to find the time with only other info given

    Any help would be appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    basic equation ...

    $\displaystyle y = y_0 e^{kt}$ , where $\displaystyle y_0$ is the initial population

    $\displaystyle y = 300e^{kt}$

    at $\displaystyle t = 4$, $\displaystyle y = 5000$

    $\displaystyle 5000 = 300e^{4k}$

    solve for $\displaystyle k$ ...

    $\displaystyle \frac{3}{50} = e^{4k}$

    $\displaystyle \ln\left(\frac{3}{50}\right) = 4k$

    $\displaystyle k = \frac{1}{4}\ln\left(\frac{3}{50}\right) \approx -0.70335...$

    if you have a store capability in your calculator, store this value in $\displaystyle k$.

    $\displaystyle 20000 = 300e^{kt}$

    $\displaystyle \frac{3}{200} = e^{kt}$

    $\displaystyle \ln\left(\frac{3}{200}\right) = kt$

    $\displaystyle t = \frac{1}{k}\ln\left(\frac{3}{200}\right) \approx 5.971$ hrs
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Growth and Decay
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: May 23rd 2011, 03:03 AM
  2. Exponential Growth and Decay
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: Jun 6th 2010, 04:42 AM
  3. Exponential Growth & Decay
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 11th 2007, 08:33 PM
  4. exponential growth and decay
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 27th 2007, 06:14 AM
  5. [SOLVED] Exponential growth + decay
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 22nd 2006, 11:22 AM

Search Tags


/mathhelpforum @mathhelpforum