An Exponential Growth Problem

[sapina12]

Thankyou! Now I understand how to solve problems like this. And I will be able to answer my exam tomorrow :))

[TheBsuperstar]

How did you get 11.5129

[HamudiChi]

THANK YOU !! I love you man. MY TEACHER TOLD US GUESS, and not use log since it was for grade 12!

I like studying online I understand better lol

[patrickJMT]

@HamudiChi you are always allowed to read / work ahead if you are so inclined : ) keep up the hard work

[ian559fresno]

YEA

[lilmisskrys21]

awesome! A big help! Thank you :)

[patrickJMT]

@lilmisskrys21 you are very welcome ; )

[BadriahTube]

exponential growth /decay problems are not my friend. I understand them but can't get the right answer...

[sarazuu]

how old are you? aha

[sarazuu]

how would you do this using logarithms instead of natural logarithms?

[sarazuu]

why do you use natural logarithms, why not just logarithms?

[TheNumber2Pencil546]

why arent you using Ce^(kt)?

[patrickJMT]

@TheNumber2Pencil546 that is for continuous exponential growth; not all exponential growth has to be continuous though. this is an example of an annual growth rate

[lucKmarquEVeINdour]

seriously, it's super funny when i used this equation and i got the different answer from my friends 0.0

[RabidCycler]

Thank you for posting this.

[nikvenkata]

" MAYBE THERES PLENTY OF NUTRIENTS"

[jaystarz72]

wasn't it in half hours?????

[JakesTechBox]

Thanks so much! I have my final tomorrow and no one could help thanks :D

[jayjok12]

thanks, This session was very helpful... I had to skip a week of class due to the flu, thanks to you I am able to catch up !!!!!

[360ketchup360]

Thanks very much!

[vugina123]

dude, you know your fuckin' math! props to helping the struggling slackers! :D

[ArenThomasian]

your THE best

[ItsSword]

Did you take Ap math exams in highschool? If you did, was your score on them a 5? Just wondering and in awe of your math skills :D

[patrickJMT]

@ItsSword no, i was very unmotivated in high school. i stopped at precal my junior year and did not take math my senior year. mainly i skipped most of my senior year. i took an english class at the community college and when it was over (two months or so), we just kept leaving. we would drive 45 minutes to go to louisville and hang out for a few hours til we had to be back for late lunch. never studied for the ACT either; i just took it. did not care about college, just wanted some freedom.

[ItsSword]

@patrickJMT

You rebel! :P

[patrickJMT]

@ItsSword hardly

[scottk812]

@patrickJMT Sounds like me in HS. I got too much freedom. So much, in fact, that I ended up giving it all away and joined the Navy! Oh well, now I get to go to college for free and am almost done with Calc 3 (with quite a bit of help from your vids), and well on my way to a Mech E degree. Thanks for the useful vids.

[dldmsqls]

Awesome :) Thanks :D

[kickflopguy]

tomorrow is my last exam for HS. imma OWN Trig now. THANKS PATRICKJMT!

[McWonderAzn]

can u be my math teacher. the one i hav now sucks

[benjaminbenbenben2]

what if we dont know what the intitial population is? how do we find that?

[stemcgolf]

I'll pay you €1000 to do my exams. Just have a shave and where a wig and you'll pass easy.

[brjp128]

i feel like i should pay your for this your amazing

[wopuga]

thanks....

[sniperboy102]

wow my proffessor used the same problem ...

[QuixoticXmischief]

Thank you thank you thank you!!!

[leo21081996]

thank you so much !it helps so much

[leo21081996]

thank you so much !

[mingos247]

Is A=Pe^rt the same as y=a(b)^t

[vepulan7]

omgsh thanks i have a test tomm, gonna live off your videos from now on. THANK YOU!

[Golvklut]

I love you right now!

[Golvklut]

I love you right now!

[xTheCheesiestx]

helped a lot thanks makes everything a lot easier

[Mrmeanjean]

Patrick, you save my life. Thank You

[The22lalala]

in y=a(1+r)^t, what does 1 represents? please reply it's urgent! :( but thanks i really appreciate it for making such awesome videos, i'm sure they helped us a LOT. :)

[wastedlove25]

,,great tomorrow is our midterm,,it helps me a lot..

[patrickJMT]

@wastedlove25 good luck on it!

[99Mandalore]

Thank You, very helpful for my project, and great example:) Thank You very much for an easy to understand, easy to learn.

[herculiest]

genius! u explained it better than my teacher!

[rohannesburg]

when can you use Ae^kt?

[patrickJMT]

@rohannesburg if you know the continuous growth rate

[Chasesk88]

thanks man you explained this much better then my teacher. [=

[annniey]

thanks!! but whats the reason for not using common logarithms?? just log not ln??

[tristanpt27]

great help!!! needed it for my math hmwk

[spenken1000]

How would you solve a problem like this where the growth rate is tripled every ten days?

[pitoria31]

hey patriick, Ive been watching your videos all the way from Colombia. Im a Math lover and Im actually coursing Ap Calculus. The AP Test is 5 days from today and I wondered if you knew where could I find some Multiple choice and free response questions to practice. Thank you for everything your videos had been really helpfull during my course.

[mllebiddies]

thank you SO much [:

[bamson101010]

LOLgarithms :)

[Soviless99]

going into logs is more advanced, you can also place the 1,000,000 in y1 on your graphing calc, then place the 10(2)^x in the y2 and graph and find where they interset (2nd trace,then 5:intersect and just hit enter twice) correct me if i am wrong but i think thats it!

[ChristinaElite]

Math is so hard!

This helped a lot with my 8th grade Algebra 1 class..

Thanks!

[lovebugg327]

thankks soo much, your videos have saved me so many times. I would have failed if i didnt use your vids while i was out sick! :)

[dunawaykb]

This helps out a lot. THX!

[Lunchsacks]

my teacher does this: (where P= population and k= related growth rate)

P(t)=Pinitial e^kt

what is k????????? and how do i find it?????

[JzzdInMyPant]

@Lunchsacks

K is a constant value, and you solve for it by using algebra

start with s = s0e^kt

divide by s0 on both sides

take the natural log of both sides

then divide by t

[JzzdInMyPant]

@Lunchsacks

ah forgot to say, the P (the population) is basically the same as the s (value) in what i wrote and the Pinitial (population initial value) is the same as the s0 (initial value) i wrote.

[Channypogosticks]

how can you find the growth factor if you are not given how much is dividing each hour?

[Applepros]

im an 8th grader... do i need to know the ln formula? when would i learn it?

[clehneis]

there is no ln formula. ln is a natural log so you can manipulate equations with exponents. You'll be fine.

[sullivanseven]

You must be crazy! how come you know everything? I was just struggling with this for hours. I don't understand why some become teachers that can't teach. You know what? You have to set up an institute for training teachers and ask the government to help you to make it mandatory for everyone who wants to become a teacher to pass a course of teaching.

Thanks my cyber friend :)

[faenda]

this is what i do:

y = initial population * growth factor^time

1000000 = 10 * 2^x

1000000/10 = 2^x

lg100000 = lg 2^x

lg100000 = x * lg 2

lg100000 / lg2 = x

x = 16,6

[kevoo37]

I do:

log100000 / log2

that gives you 16.6

[happieholly]

THANKYOU SO MUCH.

i could understand this in ten minutes by you, but i couldnt in a week of my blabbering teacher.HAHA

=)

[mynd66]

Isn't this related to why things such as weather predictions cannot be known too far in advance because tiny signals in the present grow exponentially into something our limited forcast won't detect? hence the butterfly effect

[patrickJMT]

yep! too many variables interacting in too many complicated ways that we do not fully understand!

[itsxirock]

Thanks you really helped me out...I remember seeing in class a problem where the exponent has two variables how would u solve that?

[patrickJMT]

well it just depends on what other info was given!

[itsxirock]

tru tru...I mean if the formula: y=a(1+r)e^ -kt

[supatails135]

I know about the exponential decay process but never heard of exponential growth! Thanx! ^_^

[LukasVlcek]

a=10 but here (5:45) you say that we start with 2.

[supatails135]

lol i noticed that aswell XD

[snowblazer12]

thanks =]

this was a nice review

[khooee82]

thanks :-)

[parvinhasan]

can u please make a video on logistic growth?

[parvinhasan]

thanks for the video..i was waiting for it..

[electriciansmate]

Well explained Patrick. Always find radioactive decay and body temperature more difficult.

[patrickJMT]

you are using log base 10, i use log base e....

it does not matter which base you use, so long as you use the same thing on both sides!

[TheDuskMar]

you could always use log, but you should use

log 100000 divided by log 2

[TheDuskMar]

The change of base formula is always helpful here!

Let x >0 , b > 0, and a >0

Log a (x)

-------------- = log b (x ), which is essentially

Log a (b)

what he did with the natural log. It really does simplify logarithms =]

[patrickJMT]

yep! change of base formula is what justifies the idea that it does not matter which base we use when introducing logarithms to help us solve the equation!

thanks DM

[shimirai21]

thank you very much :)

be smart ... LOL

[gellybelly2]

Thanks Pat. Nice explanation and example. I'll be glad to see the exponential decay vids soon too.

Cheers.

[quynhho2002]

because you need to do ln, not log

[manoj0072006]

hey your videos are in Hd good luck

[ilovepatrickjmt]

i wish you would grow exponentially inside of me

: )

mmmmmmm

that would be nice!

[alanna4858]

that is f'ed up my friend. wth? i think i can hear this guy getting a restraining order as I write this. hahaha. seriously, you are wrong.

Great video btw. thanks.

[patrickJMT]

wow