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Math Help - Exponential function

  1. #1
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    Exponential function


    The half-life of the radioactive element Radium-226 is 1590 years. This means that after 1590 years only half of the original radioactive material will have disintegrated. Because the
    rate of decay is proportional to the amount of material present, the function that describes this decay will be exponential.


    If the initial amount of Radium-226 present was 100g, write an exponential function, call it R(t), that describes the decay over t years, at a decay rate of k.
    .
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Snowboarder View Post
    The half-life of the radioactive element Radium-226 is 1590 years. This means that after 1590 years only half of the original radioactive material will have disintegrated. Because the
    rate of decay is proportional to the amount of material present, the function that describes this decay will be exponential.


    If the initial amount of Radium-226 present was 100g, write an exponential function, call it R(t), that describes the decay over t years, at a decay rate of k.
    .
    k = \frac {\ln 2}{T} where T is the half life.

    From there it is simple. the equation is of the form R(t) = R_0e^{-kt}

    you know what R_0 is right?

    I hope you can derive the formulas I gave you above. If not, it is a good exercise to try
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  3. #3
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    thx a lot
    So is it something like:

    50 = 100e^{-k*1590} ???
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Snowboarder View Post
    thx a lot
    So is it something like:

    50 = 100e^{-k*1590} ???
    no.

    R_0 is the initial amount, so it is 100

    R(t) stays as it is, it is just the amount after time t

    as i said, k = \frac {\ln 2}{1590}, so there should be no "k" appearing in your formula

    t is just time, it stays as is.

    Please look up what each variable represents.
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  5. #5
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    i need also show that k = -0.000436 so

    Ro/2 = Roe^-kt
    ln(0.5) = -1590k
    k = ln(0.5)/(-1590)
    k = - 0.000436

    is it correct??
    Thank you a lot
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