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 Posted: Thu Oct 11, 2007 8:23 pm
Even after getting into math courses so... "elevated"... that do all sorts of crazy things with calculus... you can't forget your algebra...
Yeah... that's right... Sibby's stuck at the end of problem 3 on his homework because he can't remember what the hell to do with exponents...
You heard right... smart-assed Sibby's having problems with exponents...
._.( )
No, chewed through the calc part of the problem without a problem... had fun with the "normal" algebra up to the point... then he hit
x * e^(-2x) = 15/7
And I swear... if I hear ANYONE say "where am I gonna use this?"... I'm going to kill someone... with my dE book... and it will involve blood. stare
Y'know why? Because this "issue" came about not as he was learning the math... no, this is part of the "word problem applied math" homework... and this problem here was to figure out how long before all the fish get fished out of an area... then, after I get this, I gotta figure out a number that the fishermen can fish so that the population of the fish doesn't die off...
And there's more... radioactive decay/c-14 dating... more population figures... air drag and speed (figuring out how long a skydiver has if his parachute doesn't open, before he dies... n_n) and plenty more...
It may seem amazing, but I see more calc in everyday life than I do algebra... and that's saying something... ^_^( )
In any case, Sibby's gonna go back to fuming worthlessly at his homework...
T__T
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Posted: Thu Oct 11, 2007 8:48 pm
That seems really really familiar. Probably when I was awake during a class or something. XD
Isn't it log that brings exponents to the basic term level? So what you'd need to do is divide by x then just log the equation and solve.
I think.
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Posted: Thu Oct 11, 2007 9:00 pm
well, with e's, it'd be the natural log function...
and if I did that... it'd be
-2x = ln(15/17x) or -2x = ln(15) - ln(17) - ln(x)
the ln(15/17) isn't a problem... but I'm in pretty much the same position with ln(x) and -2x again...
So I'm still stuck in my position...
._.( )
Thanks for helping though... chances are the solution does involve some type of natural log manipulation or something... x_o
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Posted: Thu Oct 11, 2007 9:06 pm
Well, right now I'd want to say solve the natural logs of 15 and 17, divide everything by -2 then say it's just a function of x.
But that's crazy talk.
Check the back of the book?
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Posted: Thu Oct 11, 2007 9:14 pm
 You gotta use bases. All I know. I haven't done math in 3 years.
~<3
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Posted: Thu Oct 11, 2007 9:24 pm
Druki Well, right now I'd want to say solve the natural logs of 15 and 17, divide everything by -2 then say it's just a function of x. But that's crazy talk. Check the back of the book? It's teacher made up problems... x_o Well... in that case... it'd be -2x + ln(x) = ln(15/17) If I tried raising both sides on the e... e^(-2x) + x = 15/17... which is where I began... So, back a step... -2x + ln(x) = ln(15/17) *just treat ln(15/17) as a number, since it's nothing special, like the x's... x_o So, what do I do with -2x + ln(x) ? o.O( )
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Posted: Fri Oct 12, 2007 8:43 pm
D'oh... Sibby's an even bigger idiot than he thought...
Well, he found a "internet algebra solver" thingy... and it turned up one of those "a+bi" answers... which puzzled Sibby for a while... then it hit him...
That equation is to find the time in which the population reaches zero... which the question asked... what if the population doesn't reach zero? o_o
So, he goes back to the original "equation" of 7e^2x - 15x ... and starts punching in numbers... none of which come close to zero... and actually get further and further away as x increases (meaning, the fishing doesn't do much over the long term...) this leaves Sibby thinking that it doesn't go to zero, but how to prove that...
Well, figure out when the lowest population is... and looking at the equation, it appears to have a negative slope at first, then goes to positive... and the lowest population will happen when it stops having the negative slope, but before the positive slope... meaning the slope equals zero...
Back to the calc part... that means that d/dx = 0... so, he takes the derivative to get 14e^2x - 15 and finds that the time in which the population was the lowest was x ~ .03 years... So he takes that plugs it back into the original equation, and finds that the population never dips below 6.7mil or so... o_o
Basically, under the constraints of the problem, the fishermen start to fish these fish... and the fish instead breed so fast that they soon begin to run out of water, and come on land, and start eating people... and reproducing so fast that they eventually cover the planet in fish... ^_^( )
*which, using the malthusian model the question asked for, is entirely possible, since it doesn't account for a max sustainable population... which is corrected in the logistic model...
In essence, Sibby's "equation" there he was asking about, wasn't solvable... (though, it could have been... thank God for internet resources! n_n)
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Posted: Fri Oct 12, 2007 8:49 pm
o_o ... Wha?
Sorry, English major. Not really in need of advanced math skills. Come on, I barely need intermediate math skills. I've barely mastered intermediate math skills!
Sib, you should use this and join the Mythbusters. ^^
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Posted: Sat Oct 13, 2007 5:51 am
Oh man, what do you study?
Crazy, crazy math.
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