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Math Help - Exponential Growth and Decay

  1. #1
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    Exponential Growth and Decay

    Hi, This is my first post, i couldn't find a proper category for my topic, so I'll post it here. having troubles understanding these questions...

    I have attached the two questions... thanks. They use the Q = Qo*e^kt and Q = Qo*e^-kt formula structures. Thank you very much in advance.

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  2. #2
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    For your equation

    \displaystyle Q = Q_0e^{kt}

    Substitute the points \displaystyle (0, Q_0) and \displaystyle \left(1600, \frac{Q_0}{2}\right)

    What do you get?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    For your equation

    \displaystyle Q = Q_0e^{kt}

    Substitute the points \displaystyle (0, Q_0) and \displaystyle \left(1600, \frac{Q_0}{2}\right)

    What do you get?
    um sorry? where did you get points from? I've never been taught to get points for these questions?
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  4. #4
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    I found these points from you question.

    At t=0 the amount of radioactive material is Q_0 , is this clear why?

    Now the meaning of half life is the time taken for the radioactive material to reduced to half of its original self.

    From the question, when t=1600 then the initial amount is halved i.e \frac{Q_0}{2}
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  5. #5
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    Quote Originally Posted by pickslides View Post
    I found these points from you question.

    At t=0 the amount of radioactive material is Q_0 , is this clear why?

    Now the meaning of half life is the time taken for the radioactive material to reduced to half of its original self.

    From the question, when t=1600 then the initial amount is halved i.e \frac{Q_0}{2}
    ohk, makes sense now, will give it a try. thanks
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  6. #6
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    Quote Originally Posted by MathsBeforeBedtime View Post
    ohk, makes sense now, will give it a try. thanks
    Good to hear, let us know how you go.
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  7. #7
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    Quote Originally Posted by pickslides View Post
    Good to hear, let us know how you go.
    turns out I didn't get it. my tutor said for part a), do 500 / 1600 to get 0.3125 = 31%, then just do 50% - 31% = 19%

    for part b) my tutor said to go from 100% to 50% that's a half life so it = 1600 years, then to go from 50 to 25% that's another 1600 years and so now we are at 75%. 1600 + 1600 = 3600 years.

    turns out you didn't need to use the formula for this question, bit weird. but makes kinda sense this way.

    qs 14 I do not know.
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