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Math Help - Either I'm wrong or the book is!

  1. #1
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    Either I'm wrong or the book is!

    Hi guys!

    Here's the problem (fairly simple but I'm still getting it wrong with the book's result...):

    A yearly output of a silver mine is found to be decreasing by 25% of it's previous year's output. If in a certain year it's output was 25,000,000 what could be reckoned as it's total future output...

    the book gives me 3.3 x 10 to the power 7.

    Is that right?

    Thanks!
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  2. #2
    Member mohammadfawaz's Avatar
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    Hello,

    I'm not sure I totally understood the problem but from what I could catch:
    If the output was y_n at year n, then the output will be y_{n+1} = 0.75y_n at the following year since we have a decrease by 25%. The question is asking for the total future output. What we have is a geometric sequence with a first term of 25,000,000 and a ratio of 0.75. The total sum of of this sequence is given by \frac{25,000,000}{1-0.75} = 100,000,000 (since we are summing to infinity). The answer of the book seems to be wrong unless I misunderstood the problem. By the way, is this the value you are getting??
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  3. #3
    Member u2_wa's Avatar
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    Quote Originally Posted by Mister77 View Post
    Hi guys!

    Here's the problem (fairly simple but I'm still getting it wrong with the book's result...):

    A yearly output of a silver mine is found to be decreasing by 25% of it's previous year's output. If in a certain year it's output was 25,000,000 what could be reckoned as it's total future output...

    the book gives me 3.3 x 10 to the power 7.

    Is that right?

    Thanks!
    Hello Mister77

    Correct answer in my view: \frac{3}{4}*25000000 would be the next year's output

    Book answer according to me is wrong.
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  4. #4
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    Yes that's exactly what I applied the (sum to infinity) and I got the same result 100,000,000. I get the impression that the book does a lot of wrong wording, so I tried to look at it in a different way. It reffers to a "total future output".. I reckon that may possibly mean a ratio of 1.75 (in other words that would mean for the second year, total future output, would be the previous years earnings + 0.75 of this years earnings). If I apply that to the sum to infinity I end up with 25,000,000/1.75-1 = approx 33,333,333.33.

    That would be kind of similar to what the book gives me as a result (3.3 x 10 to the power 7). But I really don't know if this is just a coincidence based on guess work or how it should be!
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  5. #5
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    Someone help!
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  6. #6
    Member mohammadfawaz's Avatar
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    Hello,

    I think the books contains an error: either in the question or in the answer. If the question is as it is, the answer is definitely 100,000,000. Trust me! The answer cannot be 3.3 \times 10^7 unless the decrease is 75% per year and not 25% because then the answer would be \frac{25,000,000}{1-0.25} = 3.333\times 10^7 which is fairly close to the answer of the book. The method we are using is correct so be confident and use 100,000,000 as an answer.

    Regards,
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  7. #7
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    Quote Originally Posted by mohammadfawaz View Post
    Hello,

    I think the books contains an error: either in the question or in the answer. If the question is as it is, the answer is definitely 100,000,000. Trust me! The answer cannot be 3.3 \times 10^7 unless the decrease is 75% per year and not 25% because then the answer would be \frac{25,000,000}{1-0.25} = 3.333\times 10^7 which is fairly close to the answer of the book. The method we are using is correct so be confident and use 100,000,000 as an answer.

    Regards,
    Thanks mohammadfawaz! Yep, I copied it exactly from the book. So at this point, I guess it has to be wrong. Thanks!
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