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Math Help - Need help with logarithm/exponential functione problems(2)

  1. #1
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    I'm in pre-calculus and I'm completely clueless with these 2 problems.
    1) The radioactive isotope of carbon-14c has a half life of 5730 years.
    A) What is the decay constant of carbon-14c
    B) If we start with a sample of 1000 carbon14 nuclei, how many will be left in 22,290 years time.

    2) A Piece of charcoal of mass 25g is found in the ruins of an ancient city. The sample shows a carbon-14 activity or R(t)= 4.167 decays/second.
    A) Convert the decay constant of carbon-14c from (1)(a) in terms of seconds instead of years.
    B) Find the number f remaining atoms of N(t) using the constant you found in (a)
    C) Suppose that the initial number of carbon-14c nuclei before decay is 1.63x10^12. What was the initial rate of decay ( or R initial)
    D) How long has the tree that this charcoal came from been dead?




    Okay so I'm given these equations

    N(t)=Ninitial*e^-ct

    R(t)=Rinitial*e^-ct


    Last edited by mr fantastic; April 10th 2010 at 10:30 PM. Reason: Restored deleted questions.
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  2. #2
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    Quote Originally Posted by farhadfarzadsucks View Post
    I'm in pre-calculus and I'm completely clueless with these 2 problems.
    1) The radioactive isotope of carbon-14c has a half life of 5730 years.
    A) What is the decay constant of carbon-14c
    B) If we start with a sample of 1000 carbon14 nuclei, how many will be left in 22,290 years time.

    2) A Peice of charcoal of mass 25g is found in the ruins of an ancient city. The sample shows a carbon-14 activity or R(t)= 4.167 decays/second.
    A) Convert the decay constant of carbon-14c from (1)(a) in terms of seconds instead of years.
    B) Find the number f remaining atoms of N(t) using the constant you found in (a)
    C) Suppose that the initial number of carbon-14c nuclei before decay is 1.63x10^12. What was the initial rate of decay ( or R initial)
    D) How long has the tree that this charcoal came from been dead?




    Okay so I'm given these equations

    N(t)=Ninitial*e^-ct

    R(t)=Rinitial*e^-ct

    So the equation for part 1, Since you know that your initial amount is 1/2 at time t=5730, you can assume values for your initial and final values
    i'll use 10 and 20 as an example

    1/2N(t)=Ne^(-ct)<br />
(1/2)20=20e^(-c*5730)

    Then use properties of logs to solve for c and this will be the decay rate

    Part 2, use that decay rate to determine the amount left after t=22,290
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  3. #3
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    Quote Originally Posted by xsavethesporksx View Post
    So the equation for part 1, Since you know that your initial amount is 1/2 at time t=5730, you can assume values for your initial and final values
    i'll use 10 and 20 as an example

    1/2N(t)=Ne^(-ct)<br />
(1/2)20=20e^(-c*5730)

    Then use properties of logs to solve for c and this will be the decay rate

    Part 2, use that decay rate to determine the amount left after t=22,290
    Uhm, I haven't learned that method or not used to doing that.

    Or do I just plug in the numbers?
    Last edited by mr fantastic; April 9th 2010 at 04:05 PM. Reason: Merged posts
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