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Math Help - Having trouble

  1. #1
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    Having trouble

    1)An old coin was worth 50 cents originally and has been growing exponentially in value by 15% every year. Predict the coin's value after 3.5 years


    2) Two investments are made. In one, $2500 is invested at 5% compounded annually. In other, $2000 is invested at 6% compounded annually. When will the investments have the same value?
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    #1:

    Since the coin increases $0.15/yr, then after the first year it is worth $0.575.

    0.575=0.50e^{k}

    k=ln(1.15)

    V=0.50e^{ln(1.15)t}
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Using the forumula P=P_0(1+\frac{r}{n})^{nt}

    we get the two equations

    P=2500(1.05)^{t} and

    P=2000(1.06)^{t}

    using substitution we get the equation

    2500(1.05)^{t}=2000(1.06)^t

    (1.05)^t=\frac{4}{5}(1.06)^t taking ln of both sides

    ln(1.05)^t=ln(\frac{4}{5}(1.06)^t) using log properties

    tln(1.05)=ln(4/5)+tln(1.06) isolating t

    t(ln(1.05)-ln(1.06))=ln(4/5)

    t=\frac{ln(0.8)}{(ln(1.05)-ln(1.06))}
    Last edited by TheEmptySet; March 15th 2008 at 12:47 PM.
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