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Math Help - Half-life problem: correct answer?

  1. #1
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    Half-life problem: correct answer?

    "What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

    Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."


    This what I did.

    I used the exact half-life formula:

    - log102
    _____________________
    log10(1+r)

    In this case, r= 0.25

    After substituting, I get:

    0.301030 = -2.4094
    ________
    -01250

    Am I right? I'm a bit confused..

    Thanks guys.

    [/SIZE]
    Last edited by c47v3770; August 7th 2008 at 05:13 PM.
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  2. #2
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    Quote Originally Posted by c47v3770 View Post
    "What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

    Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."


    This what I did.

    I used the exact half-life formula:

    - log102
    _____________________
    log10(1+r)

    In this case, r= 0.25

    After substituting, I get:

    0.301030 = -2.4094
    ________
    -01250

    Am I right? I'm a bit confused..

    Thanks guys.

    [/size]
    Half-life is positive ......

    Use the results in post #3 of this thread: http://www.mathhelpforum.com/math-he...ease-help.html

    Let initial mass be N_0. Substitute N = \frac{N_0}{4} and t = 10 and solve for k. Then substitute N = \frac{N_0}{2} and solve for t (using the value of k you found).
    Last edited by mr fantastic; August 7th 2008 at 08:50 PM. Reason: Corrected a typo
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Half-life is positive ......

    Use the results in post #3 of this thread: http://www.mathhelpforum.com/math-he...ease-help.html

    Let initial mass be N_0. Substitute N_0 = \frac{N_0}{4} and t = 10 and solve for k. Then substitute N_0 = \frac{N_0}{2} and solve for t (using the value of k you found).
    "Use the results in post #3 of this thread: Half-life problem. Please help "

    I'm not sure of what results to use. Could you please be a bit more specific?

    I really appreciate your help.
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  4. #4
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    Quote Originally Posted by c47v3770 View Post
    "Use the results in post #3 of this thread: Half-life problem. Please help "

    I'm not sure of what results to use. Could you please be a bit more specific?

    I really appreciate your help.
    N=N_0e^{-kt}.
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