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Math Help - Half life

  1. #1
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    Half life

    Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
    How much will you have 20 years from now? 25 years from now?


    Ok... so after 20 years it will be 1 grams right?

    but how come this equation doesn't give me the answer 1 gram?
    Z= (\frac{1}{2})^\frac{t}{10}

    What should be the correct eqution for it?
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  2. #2
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    Quote Originally Posted by cammywhite View Post
    Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
    How much will you have 20 years from now? 25 years from now?


    Ok... so after 20 years it will be 1 grams right?

    but how come this equation doesn't give me the answer 1 gram?
    Z= (\frac{1}{2})^\frac{t}{10}

    What should be the correct eqution for it?
    You forgot to multiply by the amount you started with

    y=4\left( \frac{1}{2}\right)^{\frac{t}{10}}
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  3. #3
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    Quote Originally Posted by cammywhite View Post
    Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
    How much will you have 20 years from now? 25 years from now?


    Ok... so after 20 years it will be 1 grams right?

    but how come this equation doesn't give me the answer 1 gram?
    Z= (\frac{1}{2})^\frac{t}{10}

    What should be the correct eqution for it?
    forget the 4?

    Z= 4\left(\frac{1}{2}\right)^\frac{t}{10}
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    You forgot to multiply by the amount you started with

    y=4\left( \frac{1}{2}\right)^{\frac{t}{10}}

    If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

    maybe my calculation is wrong
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by cammywhite View Post
    If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating
    Ummm not quite ...

    if t=20 we get

    y=4\left( \frac{1}{2}\right)^{\frac{20}{10}}= 4\left( \frac{1}{2}\right)^{2}=4\left( \frac{1}{4}\right)=\frac{4}{4}=1
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  6. #6
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    Quote Originally Posted by cammywhite View Post
    If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating
    not so ... remember the order of operations?
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  7. #7
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    Quote Originally Posted by cammywhite View Post
    If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

    <br />
Z(20) =4\left( \frac{1}{2}\right)^{\frac{20}{10}} = 4 \times \frac{1}{2^2} = 1<br />
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