Exponential Growth

[iWriteUinMyDeathNote]

hey this aint algebra

[ACfireandiceDC]

My brain is going to explode from watching this video...

[TheDecayingmaterial]

Hi Sal, I think you maybe should re-do this one, and start of by introducing the general formula for exponential growth y=a*b^t, (where b is the growth factor, a is the initial value) and then move on to how it's useful to manipulate this into an exponential function with base e.

I was a bit confused by this at first, and I see others in the comment section are too.

[Xenthoid]

This is the exact same problem ( problem 3) i was looking at in my book, Early Transcendentals

[gamobigz]

I think he needs to give a more intuition on how e^ln4.2 works.

[65nom]

Better to say ln(x) is the "undo" function of e^x and vice versa.. ?

 So func(inversefunc(x)) = x

[pixelated111]

thank you so much! I was stuck with this.

[MrAimsworth]

Where did the e^kt come from? Is there a formula for expo growth that i am not aware of?

[nathank16]

@MrAimsworth yes there is.

[Dnizzle7]

@MrAimsworth Well, if you're learning about expo growth, most people use the equation A=Pe^rt in which e^rt is the exact same as e^kt. Both equations are the same, just with different variables. P is the initial amount, e is the natural log to the power of (r times t). r is the rate and t is the time. I hope I answered your question!

[ricksterp34]

thanks!



[revelationsgeneral]

what math am i in? im doing logrythyms and they say it is alebra?

[dudeB15]

i dont get it

[bhz10]

there is a subliminal message in the first problem ;D

Thanks for the help

[steve3144]

your handwriting is messy but now its better in your new videos!

keep it up sal!

=D

keep it up dude!

[lizzy201292]

i dont get it......... :(

[ny1fanta]

you dont hav to use product rule when you mutilply 100e^ln....?

[Soulscarz]

this is the exact problem in my book chapter 7.3 #3 lol thank you i needed help on c

[lunacava]

very interesting, sir

[afreakenracoon]

HELP!!!

a car was bought for 25000$, each year it depreciates by 15%...

a) write an exponential formula that demostrates the cars value in (n) amount of years after it was purchased/

b) what is the cars value at the end of 3 years

c) after how many years will the value of the car be half of the original price?

PLZ HELP!!!! THANK YOU!!!

[aNonInteligentGuy]

can you pls tell me what that (e) means.

[ericjamesharlow]

Thanks man, I had to learn this for biology at UCSD and even the professor couldn't explain it as well as you did.

[euch27]

What is the significance of using e. When would one use e or not use e?

[CaptainCarthex]

@euch27 e is euler's number and has to deal with exponetial growth/decay. If ever there is a problem dealing with one of those e will be used.

[mintismile]

luvv ur vids!!

i think i understand more from here than from my actual teacher sometimes

[haha phone from dish network :P]

[undertakenheart2]

OMG, I'm so happy CNN talked about you!!!

Now whenever I don't understand what my AP Calc teacher is talking about, I can just head on over here.

I have a two test in that class tomorrow and I need your simplistic instruction.

[nikanj]

I'm just wondering why this video is in your precalc playlist. I've studied calculus before and am watching these videos to review what I've learned so I was able to follow but the I don't think this logically belongs in the playlist.

Sorry if that sounds critical. I think your videos are wonderful and just wanted to offer a suggestion.

[3balljuggler]

Wow this was the same exact problem that I was working on.

5 stars! Great video.

[alkalait]

@ redgenda: "ln^(4.2)=x" translates to "the exponent x on e (e^x) that gives 4.2". so remember, ln^(4.2) is That exponent "x".

Put now that Same exponent "x" on e (e^x) and ask yourself what would you get...

[alkalait]

sorry I didn't notice you got it. anyhow, i got to play smart :P

[RICHY940]

pothead lmao

[crodd63]

the way you do it in the states is alittle different than that of nova scotia

[angelo4chris]

thanx one more time... im taking algebra 2

[Midni6htF4iry]

thank you, it helped a lot

[WhosAlex]

AGh You scared me. I forgot This window was open when it started playing.

[raidtothegrave]

i get X !!!!!!

[marcusjhung]

good stuff, Salman

[uburex97]

Confused.

Thought this was pre-calculus but you meed to take a derivative....Back to the beginners class

[WaffleSharpie]

lol have no idea what he's saying and im taking honors pre calc. next year in 10th -.-

[knmhb22]

@WaffleSharpie

I too am taking  honors pre-calc.

please don't use derogatory comments as a way of showing ur opinions...he's doing a great thing..any way, its ur choice whether or not to watch his videos or not. ;)

[WaffleSharpie]

LOL. Sorry thats not what I meant I'm saying in between the lines that I hope I can make it next semester and get an A. I actually like his video. I'm just very confused because I'm not in that class yet and I just picked a random video without any experience in Pre Calc. I'm going to watch these videos when I'm in it Next year. sorry If it sounded like a derogratoty comment. I seem to offend many people when I type. kind of hard typing every little detail on how I feel w/o making it sound bad.

[armlessmcgurk]

t-t-t-t-today junior!!!

[Piscivorus]

I totally didn't follow. But since bacteria divide by 2 every reproductive cycle, 100 becomes 200 which becomes 400 etc. 420 is at the very beginning of the 3rd cycle. It's 20/400 which = 0.05 or 5% of the 3rd cycle so, 1 hour is 2.05 reproductive cycles. 60 minutes/2.05 = 29.268 minutes per cycle. 180 minutes/29.268 minutes= 6.15 cycles in 3 hours- (1) 100->200, (2)200->400,(3)400->800,(4)800­->1600,(5)1600->3200,(6)3200->­6400, and (6400*0.15)= 7360 bacteria after 3 hours.

... I think. :)

[Piscivorus]

...i forgot to do the last part. In the 7th cycle the population goes from 6400 to 12800 so, the population reaches 10000 before the 7th cycle finishes. The difference between 6400 and 10000 is 3600 and 3600/6400 = 0.5625 or 56.25% of the way through the 7th cycle. A cycle is 29.268 minutes and 0.5625*29.268 = 16.46325 minutes so, it takes (6*29.268 minutes) + 16.46325 minutes = 192.07125 minutes = 3.2 hours = about 3 hours and 12 minutes for the population to reach 10000. :)

[mrNasty8]

this is exponential growth Retard

[Piscivorus]

stupid says what?

[roketboyd]

wow. u are so easy to listen to. amazing. Really. Everything u say gets sunk into my mind. So simple, so genius. Thanks much Sir.

[spartanman8393]

great video i learned alot

[brco2003]

b(t)=100(4.2)^t

Wouldn't this be a simpler form of the expression for the number of bacteria after t hours?

[gdawgrapper]

I was wondering myself, but he did eventually get there around 10 min. For me, it's like you, a heck of a lot more understandable as b(t) = 100(4.2)^t. And if that wasn't intuitive enough, take the points (0, 100), (1, 420), and (2, 420*4.2) and plot them, then run an exponential regression to find the equation and from there be able to more easily answer all the questions--but that goes into graphing calculator proficiency.

[Pluffo]

Did you watch the whole video?

[marcellohro]

yes it would

[jdrizd2]

exponential decay? Have you developed a mathematical expression for describing the imminent loss of penicillin?

[brco2003]

hahah the phone that was brilliant! ur the best!

[AkashP4]

Thank you!