Thread: Either I'm wrong or the book is!

1. 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!

2. 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??

3. 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.

4. 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!

5. Someone help!

6. 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,

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