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Math Help - Need serious help with midtern review questions.

  1. #1
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    Need serious help with midtern review questions.

    serious issues with some problems.

    1. The ABC corporation issues a bond that pays 10,000$ after 10 years. If the initial investment is 5,000$ what is the interest rate per year, compounded annually.

    The equation to use is A = P ( 1 + r )^t

    Where A = Ending amount
    P = Starting amount
    r = interest rate
    t = time

    Right now I have this
    10,000 = 5,000 ( 1 + r ) ^ 10
    2 = ( 1 + r ) ^ 10
    <br />
Log_((1+r)2=10

    But i'm not sure where to go from here. Any ideas?


    2. Mary wants to invest money in a 7-year saving certificate with an interest rate of 6% per year, compounded continuously. How much will she need to invest to have $1000 at the end of the term.

    This uses the equation A = Pe^rt Where all variables have the same value is before, and of course e is e (2.7.........)

    So far I have
    1000=Pe^(7 x .06)
    1000=Pe^.42
    ln(1000)/ln(.42)=lnP

    And now I have no idea what to do


    3. Write the estimate in exponential form (Using the definition of a logarithm)

    ln10 = 2.303

    With this one I have absolutely no idea what I should do.


    4. A water filter is constructed from a foam that REMOVES 25% of impurities for each inch of foam. How many inches of foam are needed for the filter to remove 50% of the impurities.

    I know that this can be modeled with A = Pa^x and also with A = Pe^(rx)


    P = concentration of impurities before filtration
    A = concentration of impurities in filtered water
    x = thickness of foam

    I understand that .5P  = Pa^x

    But I can't move much further from there.



    Please don't just give answers. I really need to understand how to solve each problem. Thank you in advance.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Yelfett2 View Post
    serious issues with some problems.

    1. The ABC corporation issues a bond that pays 10,000$ after 10 years. If the initial investment is 5,000$ what is the interest rate per year, compounded annually.

    The equation to use is A = P ( 1 + r )^t

    Where A = Ending amount
    P = Starting amount
    r = interest rate
    t = time

    Right now I have this
    10,000 = 5,000 ( 1 + r ) ^ 10
    2 = ( 1 + r ) ^ 10
    <br />
Log_((1+r)2=10

    But i'm not sure where to go from here. Any ideas?


    2. Mary wants to invest money in a 7-year saving certificate with an interest rate of 6% per year, compounded continuously. How much will she need to invest to have $1000 at the end of the term.

    This uses the equation A = Pe^rt Where all variables have the same value is before, and of course e is e (2.7.........)

    So far I have
    1000=Pe^(7 x .06)
    1000=Pe^.42
    ln(1000)/ln(.42)=lnP

    And now I have no idea what to do


    3. Write the estimate in exponential form (Using the definition of a logarithm)

    ln10 = 2.303

    With this one I have absolutely no idea what I should do.


    4. A water filter is constructed from a foam that REMOVES 25% of impurities for each inch of foam. How many inches of foam are needed for the filter to remove 50% of the impurities.

    I know that this can be modeled with A = Pa^x and also with A = Pe^(rx)


    P = concentration of impurities before filtration
    A = concentration of impurities in filtered water
    x = thickness of foam

    I understand that .5P = Pa^x

    But I can't move much further from there.



    Please don't just give answers. I really need to understand how to solve each problem. Thank you in advance.
    HI

    (1) You can rewrite 2 as (2^{\frac{1}{10}})^10

    (2^{\frac{1}{10}})^10=(1+r)^10

    Comparing , 2^{\frac{1}{10}}=1+r

    r=2^{\frac{1}{10}}-1

    (2) 1000 =Pe^{0.42}

    P=\frac{1000}{e^0.42}

    where here you could use your calculator since e has a value instead of taking the logs .

    (3) a^x=y\Rightarrow log_a{y}=x

    so here \ln 10=2.303 ..... e^{2.303}=10


    By the way , you should only post one question per thread . This is one of the rules of the forum.
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    HI

    (1) You can rewrite 2 as (2^{\frac{1}{10}})^10

    (2^{\frac{1}{10}})^10=(1+r)^10

    Comparing , 2^{\frac{1}{10}}=1+r

    r=2^{\frac{1}{10}}-1

    (2) 1000 =Pe^{0.42}

    P=\frac{1000}{e^0.42}

    where here you could use your calculator since e has a value instead of taking the logs .

    (3) a^x=y\Rightarrow log_a{y}=x

    so here \ln 10=2.303 ..... e^{2.303}=10


    By the way , you should only post one question per thread . This is one of the rules of the forum.
    Thank you.

    Thats a rather odd rule dont you think? Better to have 1 thread with 4 questions than 4 threads with 1 question.
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  4. #4
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    Ottawa, Canada
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    Quote Originally Posted by Yelfett2 View Post
    Thats a rather odd rule dont you think? Better to have 1 thread with 4 questions than 4 threads with 1 question.
    Well, when you start your own site, then put in that rule.
    To each his own.
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  5. #5
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    Quote Originally Posted by Yelfett2 View Post
    Thank you.

    Thats a rather odd rule dont you think? Better to have 1 thread with 4 questions than 4 threads with 1 question.
    Think about it. Threads can get convoluted and difficult to follow (from all the replies) when there are too many questions.
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