Results 1 to 3 of 3

Math Help - Carbon-14 Half-life word problem

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    31

    Carbon-14 Half-life word problem

    Anyone know how to go about solving a problem like this?

    Yesterday the Holy Grail was found in my lawn. Knowing the Grail must be 2,000 yrs old and Carbon-14's 1/2 Life is 5,700 yrs, what % must be gone to be real
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by cjmac87 View Post
    Anyone know how to go about solving a problem like this?

    Yesterday the Holy Grail was found in my lawn. Knowing the Grail must be 2,000 yrs old and Carbon-14's 1/2 Life is 5,700 yrs, what % must be gone to be real
    What a coincidence! i found the Grail in my backyard just last week. mine is the real one of course.

    Let A(t) be the amount of carbon-14 remaining at time t, let A_0(t) be the original amount of carbon-14. since we lose carbon-14 in an exponential decay, we have that:

    A = A_0e^{-rt}

    where r is the rate of decay and t is the time elapsed.

    now, we know that r = \frac {\ln 2}{t_h} where t_h is the half-life

    thus we have:

    A = A_0e^{\frac {\ln 2}{5700}t}

    now assume we have 1 unit to begin with. then the A remaining after 2000 years (in the decimal form of a percentage) is given by:

    A = e^{\frac {\ln 2}{5700}(2000)}

    now calculate that
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by cjmac87 View Post
    Anyone know how to go about solving a problem like this?

    Yesterday the Holy Grail was found in my lawn. Knowing the Grail must be 2,000 yrs old and Carbon-14's 1/2 Life is 5,700 yrs, what % must be gone to be real
    The amount remaining given an initial amount A_0 after time t if t_{HL} is the
    half life is:

     <br />
A(t)=A_0 2^{-t/t_{HL}}<br />

    In this case let A_0=100.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. half life word problem using logs
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 1st 2009, 12:06 PM
  2. half-life word question
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 14th 2009, 01:05 AM
  3. Word problems, half life ...
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 15th 2009, 03:36 AM
  4. Half-Life problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 26th 2008, 03:27 PM
  5. half life problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 11th 2007, 04:25 PM

Search Tags


/mathhelpforum @mathhelpforum