Results 1 to 3 of 3

Math Help - exponential decay

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    11

    exponential decay

    Five grams of a certain radioactive isotope decay to three grams in 100 years. Assuming that the rate of decay is proportional to the amount present, after how many more years will there be just one gram?

    Now assume that the rate of decay is proportional to the square of the amount present. After how many more years will there be just one gram?

    i found 315 and 600 but theyre wrong. any help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by keemariee View Post
    Five grams of a certain radioactive isotope decay to three grams in 100 years. Assuming that the rate of decay is proportional to the amount present, after how many more years will there be just one gram?

    Now assume that the rate of decay is proportional to the square of the amount present. After how many more years will there be just one gram?

    i found 315 and 600 but theyre wrong. any help?
    We know that since it is proportional to itself it will follow the formula

    y=Ce^{kt}

    We see that t=0 y=5

    So 5=Ce^{5\cdot{0}}\Rightarrow{C=5}

    Next we know that at t=100 y=3

    So 3=5e^{100k}

    so \ln\bigg(\frac{3}{5}\bigg)=100k\Rightarrow{k=\ln\b  igg(\sqrt[100]{\frac{3}{5}}\bigg)}

    So we know have

    y=5e^{\ln\bigg(\sqrt[100]{\frac{3}{5}}\bigg)t}

    and you want to solve 1=5e^{\ln\bigg(\sqrt[100]{\frac{3}{5}}\bigg)t}

    how would you do that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,086
    Thanks
    375
    Awards
    1
    Quote Originally Posted by keemariee View Post
    Five grams of a certain radioactive isotope decay to three grams in 100 years. Assuming that the rate of decay is proportional to the amount present, after how many more years will there be just one gram?

    Now assume that the rate of decay is proportional to the square of the amount present. After how many more years will there be just one gram?

    i found 315 and 600 but theyre wrong. any help?
    You mostly have the answer for the first one correct. Re-read the question: "...after how many more years will there be just one gram?" So your answer would be 315 - 100 = 215 years. This is the same error that you made in the second problem.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Decay
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: April 15th 2013, 12:19 AM
  2. exponential decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 22nd 2010, 11:03 PM
  3. Decay rates in exponential decay
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 21st 2009, 06:20 AM
  4. Exponential Decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 11th 2008, 06:48 AM
  5. Exponential decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 31st 2008, 08:33 AM

Search Tags


/mathhelpforum @mathhelpforum