# Either I'm wrong or the book is!

• Feb 28th 2010, 03:16 AM
Mister77
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!
• Feb 28th 2010, 03:37 AM
Hello,

I'm not sure I totally understood the problem but from what I could catch:
If the output was $\displaystyle y_n$ at year n, then the output will be $\displaystyle y_{n+1} = 0.75y_n$ 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 $\displaystyle \frac{25,000,000}{1-0.75} = 100,000,000$ (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??
• Feb 28th 2010, 03:40 AM
u2_wa
Quote:

Originally Posted by Mister77
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: $\displaystyle \frac{3}{4}*25000000$ would be the next year's output

Book answer according to me is wrong.
• Feb 28th 2010, 04:12 AM
Mister77
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!
• Feb 28th 2010, 10:01 AM
Mister77
Someone help!
• Feb 28th 2010, 10:09 AM
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 $\displaystyle 3.3 \times 10^7$ unless the decrease is 75% per year and not 25% because then the answer would be $\displaystyle \frac{25,000,000}{1-0.25} = 3.333\times 10^7$ 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,
• Feb 28th 2010, 01:42 PM
Mister77
Quote:

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 $\displaystyle 3.3 \times 10^7$ unless the decrease is 75% per year and not 25% because then the answer would be $\displaystyle \frac{25,000,000}{1-0.25} = 3.333\times 10^7$ 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.