Results 1 to 4 of 4

Math Help - exponential growth

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    exponential growth

    Hi, I'm having trouble using the formula for exponential growth when finding the half-life.

    Q: A sample of Bismuth-210 decayed to 33 percent of its original mass after eight days.

    find the half life of this element and then find the mass remaining after 12 days.

    The formula that I am required to use for this question is:
    y_t=y_o(e)^(kt)

    I cannot simply use the half-life formula aka: y_t=y_o(0.5)^(t/h).

    I know for this general exponential growth formula that I must find the value of k, the constant first... and when dealing with the half-life. So here is my work, but it is not right.. as it does not match the answer in the back.

    I took half of the initial amount: so.. 100-33=67 therefore 67% left... half of that is 33.5% left so
    33.5=100(e)^(8k)
    ln0.335=lne^(8k)
    k=ln0.335/8
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by skeske1234 View Post
    Hi, I'm having trouble using the formula for exponential growth when finding the half-life.

    Q: A sample of Bismuth-210 decayed to 33 percent of its original mass after eight days.

    find the half life of this element and then find the mass remaining after 12 days.

    The formula that I am required to use for this question is:
    y_t=y_o(e)^(kt)
    .33 = e^{8k}<br />

    \ln(.33) = 8k

    k = \frac{\ln(.33)}{8}


    .5 = e^{kt}

    \ln(.5) = kt

    t = \frac{\ln(.5)}{k} = \frac{8\ln(.5)}{\ln(.33)}

    half life , t \approx 5 days
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    how do i find the mass remaining after 12 days? the answer is 19% of original amount......
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by skeske1234 View Post
    how do i find the mass remaining after 12 days? the answer is 19% of original amount......
    y = e^{12k}

    with k = \frac{\ln(.33)}{8} ...

    y \approx .19 ... 19%
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Growth
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 25th 2009, 09:52 PM
  2. exponential growth
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: November 6th 2008, 07:37 PM
  3. Exponential Growth
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 1st 2008, 08:17 AM
  4. Exponential Growth
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 10th 2008, 02:54 PM
  5. exponential growth help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 15th 2007, 04:16 PM

Search Tags


/mathhelpforum @mathhelpforum