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Math Help - Quadratic Equation help

  1. #1
    Junior Member
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    Question Quadratic Equation help

    How would I solve this?

    "If a radioactive substance has a half life of 14 hours, how long would it take to reach a level of 10%"

    I have no idea how to do this, although I think I may have copied it down wrong.

    Any help please?
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  2. #2
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    Quote Originally Posted by largebabies View Post
    How would I solve this?

    "If a radioactive substance has a halflife of 14 hours, how long would it take to reach a level of 10%"

    I have no idea how to do this, although I think I may have copied it down wrong.

    Any help please?
    I am not sure it is a "quadratic" function problem.
    From what I know, it should be exponential, which has a form y = ab^t

    Half life just means the time for the intial amount decreased by a half.
    So if you start with a at t = 0,
    at t =14,(14 hours later), y is (1/2) of a which is 0.5a.
    And at t = 28, (another 14 hours later) you get (1/2) of (0.5a) which is (0.25a),
    and so forth.

    So you can either find two points by the reasoning above and obtain a formula for the exponential function. After that you can solve the equation y = 10%.

    Or if you note that b = (0.5)^(1/14) (the growth factor) by observation then we have y= a(0.5)^(t/14) and so on.
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  3. #3
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    I'm still somewhat confused but i'll just skip it for now, thanks for your help
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