An Exponential Growth Problem
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- Опубліковано 11 бер 2009
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! An Exponential Growth Problem.
In this video, I review some basics about exponential functions, and do two problems related to exponential growth.
For more free math videos, visit PatrickJMT.com
@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.
damn
I'm taking an initial credit crouse in Precalculus at Woodbury University, and we're coving a chapter a day! The lessons are ridiculously fast paced!. These videos are lifesavers! Thanks Patrick!
@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
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
@HamudiChi you are always allowed to read / work ahead if you are so inclined : ) keep up the hard work
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
Thanks Pat. Nice explanation and example. I'll be glad to see the exponential decay vids soon too.
Cheers.
@lilmisskrys21 you are very welcome ; )
Thanks for taking time to put up this video. really helpful!
Thanks a lot Patrick!God bless you!Helpful your simple explanation.
@rohannesburg if you know the continuous growth rate
As a soon-to-be first-year teacher preparing to take the Praxis II Math CK, I can honestly say that your videos have helped immensely! I like to pause the video to try out the problem myself first, and then watch to see if my solution matches yours.
@ItsSword hardly
you make it seem so simple, thanks fam
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.
THANKS SO MUCH FOR THIS VIDEO!!!! This helped me so much man, THANKS!!
@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
Thank you for posting this.
Thank you! I have my AP Calc test coming up. I have been using your videos to brush up.
I was wondering why did you use natural log to solve for t?
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 =]
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!
tomorrow is my last exam for HS. imma OWN Trig now. THANKS PATRICKJMT!
Thanks I was all confuses when watch this on Khan Academy, but you made this so much simpler.
spread the word and keep coming back! glad i could help.
Khan Academy is good if you want like a full, in-depth lesson on the subject. patricJMT is great if you just want to learn it and move along.
+blackdragon13 no one is ought to do the things for you ! you should be grateful to people for what you have. they dont charge u!
he just said he likes my explanation better. what is the problem in that?
+ally gally Wow I can't thank a person for helping me understand something better.
Hey Patrick, I figured it out. First I had to find K and them take the derivative of that with t=3. :) Thanks for responding though! The Dude and you are my heroes. ;)
@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.
Thankyou! Now I understand how to solve problems like this. And I will be able to answer my exam tomorrow :))
thanks patrick, i missed the lesson for this day and because of you i understand it now.
Thank you patrikJMT for your videos they are very helpful and well done. At 7:49, you introduce ln to solve the problem. Why is it necessary, or how does introducing ln, help us solve the problem. Tia.
helped a lot thanks makes everything a lot easier
@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.
i really like it when this guy explained that double the size is 100% with money logic. i was like 'AHA, I got it!' instantly.
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! :)
thanks =]
this was a nice review
well it just depends on what other info was given!
Can you do a question involving exponential growth if some of the population is removed? For example, bacteria population (initially 1000) doubles every hour, but during that same time 100 are removed each hour. How many are there after 3 hours (assuming the growth and removal are all continuous over the time period)?
Thanks very much!
omgsh thanks i have a test tomm, gonna live off your videos from now on. THANK YOU!
you made this so easy for me! thanks. the only thing i don't understand is how (b) in the first example = (1+r) in the second.?
not sure what you mean: rate of bacteria. the growth rate is just the r value
Thank you so much!
Well, the question in particular that I am asking about is a bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After one hour the population has increased to 420. It is a four part question. I can find the number of bacteria. The formula, and when the pop. will reach 10,000 but I can't figure out the "rate growth" after 3 hours. That is what I meant when I tried to refer it to your sample problem. Obviously I have a concept error.Sorry for the confusion.
yep! too many variables interacting in too many complicated ways that we do not fully understand!
Thank you so much, u r the man for the job,Mashallah
just one point, why sometime we use e and sometimes like in this video we didnt use e, can you explain to me, Thank you,
thanks man you explained this much better then my teacher. [=
You could you solve part b) with a table. Because in our class MCR 3U we solve it with a table. So I really want to understand how to solve without log. Thank you so much for your video. It does help me a lot.
thanks!! but whats the reason for not using common logarithms?? just log not ln??
Sorry...
Could you solve part b) with a table. Because in our class MCR 3U we solve it with a table. We did not cover log yet. So I really want to understand how to solve without log. Thank you so much for your video. It does help me a lot.
Isn't y=ae^bt the formula of expo growth?..
yes that he doesnt explain.
Thank you thank you thank you!!!
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!
My bio teacher is showing us this... I'm in the beginning of algebra 2... You lost me at the log part. xD Besides that, thank you~
How do you solve it when you are trying to find the percentage?? Also how to you type it into the calculator???
Hey Patrick,
I looked at all you vids on exponential decay/ half life but I still need help with this question: The half life of nitrogen is 10 minutes. Write an equation to describe the phenomenon.. (They're asking me to find the decay factor right??) Not sure what to do after this:
A (t) = Ae^ (-.5) x (10 mins)
not even sure if that's right either..
wow
You are a credit to the species.
,,great tomorrow is our midterm,,it helps me a lot..
why you give the values to variables randomly?what i mean is , lets say you had a and b. why did you consider a=10 and b=2? why not visa verse? i would appreciate if you explain why you choose your variables equal to the numbers. And why this is first and the other is second
I understood exactly what you did but my only question... isn't the exponential growth equation N(t) = N(not)e^(rt) ?
My professor never taught us this equation y=a(b)^t
@abdulrahman226 ln is the same as log base e
Thanks! I have been doing work separately at home and the book just doesn't explain this well enough.
dude, you know your fuckin' math! props to helping the struggling slackers! :D
@wastedlove25 good luck on it!
how would you do this using logarithms instead of natural logarithms?
Went through this in a lecture for 1 weeks, didn't understand anything. Watching this video and understanding in 10 minutes. holy fuck.
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
Thanks so much! I have my final tomorrow and no one could help thanks :D
i feel like i should pay your for this your amazing
Shouldn't the two In cancel each other like In(100,000) / In(2) shouldnt it be 50,000. Just wondering because we aren't supposed to use calculators
YEA
cud u explain it using the other formula where Pn=(1+r)n Po
I think taking log base 10 of 100,000 is very easy instead of taking natural log. Say log 100,000 is =5 and log of 2 ( base 10) is 0.30... Therefore t = 5/0.3 = 16.66 What say.
Hi Patrick, could you tell me please how you would figure out what the rate of bacteria is seven hours later, then please? It is so obvious, i'm sure. :S
what if we dont know what the intitial population is? how do we find that?
why arent you using Ce^(kt)?
thank you SO much [:
you should do a expo growth vid on rice/chess board problem if you haven't alredy
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?????
The last step you could just do log(100000)/log(2 = approx/ 16.61 hours, ;)
Is A=Pe^rt the same as y=a(b)^t
no, but he claims they do the same thing, very bad.
He's got great handwriting.
a=10 but here (5:45) you say that we start with 2.
seriously, it's super funny when i used this equation and i got the different answer from my friends 0.0
I love you right now!
you're the best..
How would you solve a problem like this where the growth rate is tripled every ten days?
you could always use log, but you should use
log 100000 divided by log 2
Perhaps she means the instantaneous rate of growth at 7hrs, not the relative growth rate
why do you use natural logarithms, why not just logarithms?
i tried looking up the movie growth um... not what i expected. :-/
Then it's not a Exponential Growth. It would be a "No Solution" or you just can't solve the Problem. For Exponential Growth you need a Starting point for it to Grow every time. (Or depending where and how you learned it it may start at 0 but thats almost always 99% not the Case)
course*
i know this guy is great but he doesnt have that many physics vids as he does with math ? anyone know where good physics videos are on youtube ? thanks!
why matimatician tutor always a right handed?
are you serious? its already hard enough not being distracted by the videos on youtube while trying to understand math, but then putting a trailer for a movie in the ads?
wtf
" MAYBE THERES PLENTY OF NUTRIENTS"
I love you
finding the growth rate is still a bit fuzzy :O
because you need to do ln, not log
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.
wasn't it in half hours?????