Scary Calc. Question.... Any help greatly appreciated

[yankeekd25]

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]

Take the limit as t goes to infinity. The exponential term goes to 0, leaving you with 6000.

[shootermcgavin7]

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]

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]

Wait, I don't think this is really a calculus problem. Looks more like plain algebra to me.

[RedSpikeyThing]

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]

the answer is F

[smitch250]

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]

I got A. Im assuming thats right...

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

[yankeekd25]

what did you get then?

[Tofer]

From now on, just go here: http://www.sosmath.com/CBB/index.php

[d'Anconia]

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]

thank u guys. i didnt mean to bug ya... just needed a little help.

[shootermcgavin7]

fatrb needs to calm down.

[SpecialK]

It seems like every math problem thread gets 10+ more replies than are necessary.

[Ron Burgundy]

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]

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

Is that a pun?

[Talking_God]

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]

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]

[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]

you don't actually have to take a limit to get the answer lol

[d'Anconia]

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]

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.