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View Full Version : Scary Calc. Question.... Any help greatly appreciated

yankeekd25
04-12-2007, 09:14 AM
A population gorws according to the equation P(t)= 6000-5500e^-0.159t for t> or equal to 0, t measured in years. This population will approach a limiting value as time goes on. During which year will the population reach half of this limiting value?

(A) Second
(B) Third
(C) Fourth
(D) Eighth
(E) Twenty-ninth

What is a limiting value?

SpecialK
04-12-2007, 10:00 AM
Take the limit as t goes to infinity. The exponential term goes to 0, leaving you with 6000.

shootermcgavin7
04-12-2007, 10:33 AM
And if you need additional info from what special K said, just take half of 6000 and solve the equation for it. You can either use logs or just plug & chug since you have multiple choice.

yankeekd25
04-12-2007, 11:18 AM
And if you need additional info from what special K said, just take half of 6000 and solve the equation for it. You can either use logs or just plug & chug since you have multiple choice.

I got A. Im assuming thats right...

d'Anconia
04-12-2007, 01:41 PM
Wait, I don't think this is really a calculus problem. Looks more like plain algebra to me.

RedSpikeyThing
04-12-2007, 03:21 PM
Wait, I don't think this is really a calculus problem. Looks more like plain algebra to me.

limit as t approaches infinity....looks like calc to me. Maybe "pre-calculus". Same ****, different pile.

Cirino83
04-12-2007, 04:52 PM

smitch250
04-12-2007, 04:57 PM
ive taken up to calc 3. yea it was fun. and yea we talked about stuff like that in calc. so id consider it a calc question.

shootermcgavin7
04-12-2007, 06:02 PM
I got A. Im assuming thats right...

Based on a quick run through my calculator, I think your assumption may be faulty.

yankeekd25
04-12-2007, 08:17 PM
what did you get then?

Tofer
04-12-2007, 08:45 PM
From now on, just go here: http://www.sosmath.com/CBB/index.php

d'Anconia
04-12-2007, 09:03 PM
God damn it. The limit is 6000 so plug in 3000 for P(t) and solve for T and you get...
t = 3.81
SO during 3.81 years you are on the FOURTH year. So 'C' should be correct and that makes yankeekd25 and Cirino83 are incorrect (Ha, just had to screw with you guys).

And yes I used my graphing calculator because why else would I ****ing buy it and not use it?

Damn your calc problem thread has been bugging me all day. DONE! FIN! Somebody lock this thread.

Sadly enough the first two replies explained how to solve it quite well.

yankeekd25
04-12-2007, 09:14 PM
thank u guys. i didnt mean to bug ya... just needed a little help.

shootermcgavin7
04-12-2007, 09:47 PM
fatrb needs to calm down.

SpecialK
04-13-2007, 01:27 AM
It seems like every math problem thread gets 10+ more replies than are necessary.

Ron Burgundy
04-13-2007, 08:01 AM
Wait, I don't think this is really a calculus problem. Looks more like plain algebra to me.

Calc is all about integration and deriving, other than knowing the rules of both it's plane algebra.

RedSpikeyThing
04-13-2007, 09:53 AM
Calc is all about integration and deriving, other than knowing the rules of both it's plane algebra.

Is that a pun?

Talking_God
04-13-2007, 01:23 PM
he probably didnt mean it to be. That is calculus because the formula to find the exponential growth/decay can be derived from something or other. I just covered it in class a few weeks ago, but i was asleep so i don't remember fully why it has to do w/ calc.

SpecialK
04-13-2007, 05:42 PM
Calc is all about integration and deriving, other than knowing the rules of both it's plane algebra.

This problem involves taking a limit. Both the derivative and the integral operations are obtained by taking limits. That is why this problem could be classified as a calculus problem.

d'Anconia
04-13-2007, 10:43 PM
[Calculus] extends [analytical geometry] by introducing the concept of the limit which allows control over arbitrarily small and arbitrarily large numbers.

While I may have been right about finding the answer, it looks like Ron and I are *technically* wrong in that limits are considered part of calculus (if we're going by Wiki's definition).

Talking_God
04-13-2007, 10:58 PM
you don't actually have to take a limit to get the answer lol

d'Anconia
04-13-2007, 11:18 PM
But then how would you know when you're at half of the maximum? Even if you don't write it on paper you have to look at it and calculate where the function would go when 't' goes toward infinity. That by definition I would think is considered taking the limit since you can't mathematically plug in infinity for 't'.

Anyway you guys are making me feel like a mentally masturbating nerd right now.

d'Anconia
04-13-2007, 11:32 PM
Or maybe you could have set it up as the ratios of the two being equal to 1/2 and then try to solve for 't' or something I guess. If you could do that then it wouldn't be calculus.