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Math Help - exponential growth and decay

  1. #1
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    exponential growth and decay

    please help?

    1. the half life of radium is 1600a. what fraction of the radium in a sample remains after 400 a?

    2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of $100 in 70 a if money earns 3.5% interest compounded annually.

    thank youu.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by checkmarks View Post
    please help?

    1. the half life of radium is 1600a. what fraction of the radium in a sample remains after 400 a?

    2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of $100 in 70 a if money earns 3.5% interest compounded annually.

    thank youu.
    what do the a's mean?

    For the first:

    Use the formula A(t) = A_0 e^{-rt}
    where A(t) is the amount remaining after time t, A_0 is the intial amount, r is the rate of decay, and t is the elapsed time.

    Also use the fact that t_h r = \ln(2) \Rightarrow r = \frac { \ln(2)}{t_h}, where t_h is the half-life

    your second question is oddly worded
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by checkmarks View Post
    2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of $100 in 70 a if money earns 3.5% interest compounded annually.
    By the way, are you sure this shouldn't be "continuous" compounding? because that would fit right into the theme we have going here
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  4. #4
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    sorry, i should've been more clear...
    a represents years (it means annum)

    and for the 2nd question, i thought the same. i dont know if the 1st part of the question is irrelevant or not.
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