Trouble with negative exponent solution

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gwys

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Sep 24, 2008
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Hello,
I am in an economics course and I can't quite remember how to solve this equation. I am trying to solve for P which is the price of the good at equilibrium, but that doesn't really matter (just boring Economics talk to you math wizzes).
The initial formula is 100+ 3p = (50,000/1,000)p^-.5

I've slimmed down the problem to 100+3p= 50/p^.5 or =50/p^(1/2)


But I can't figure out the right way to go from here, I've tried a couple of directions and the numbers don't seem right.

It would be greatly appreciated for help getting past this step that I Know should be easy.

Thanks for your time,
gwys
 
Are you sure you copied that initial equation correctly; asking because it leads to this ugly cubic:
9p^3 + 300p^2 + 10000p - 2500 = 0

Putting it through the grinder has p = .246346....
Is that roughly what the "economics class" would expect?!
 
Denis said:
Are you sure you copied that initial equation correctly[?] ...
Putting it through the grinder has p = .246346 ...
Click to expand...

Yeah, that looks about right to me, Denis.

P is the equilibrium price per penny for the US Mint to produce and release into circulation -- on President Lincoln's birthday this coming February -- each new Lincoln penny (four designs) in copper. :wink:

The figure should not surprise, since we all collectively pay our government over a nickel apiece to produce and release the plain 'ol regular Lincoln pennies.

~ Mark :)
 
Ya...you gotta hand it to them...else they'll come and take it :twisted:
 
yes I did copy it down directly from the homework assignment sheet, and believe me, I've checked, and double checked to make sure it's correct. The number is just an ugly one, and that .246346 does look like what the number should come out to be. It's no big deal I've come to find, as I talked to my prof and he said that he wont be giving as difficult questions (mathematically) on any of the examinations.

Logically I feel that .246346$ shouldn't be the price of a bottle of water, (atleast in today's market) but that is a number that appears to work with the problem. So I'll stick with that.

Thanks so much for your help!
Gwys
 
gwys said:
Logically I feel that .246346$ shouldn't be the price of a bottle of water, (atleast in today's market) ...

That sounds perfectly logical to me. Just a few days ago - I bought 12 bottles for $2.99 (16 oz. bottles).

I think its a bit pricey - that's why I save the bottles and fill it up with tap water and reuse again....

Thanks so much for your help!
Gwys
Click to expand...
 
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