@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!
makes more sense to use b(t)= I(2())^(t/r) where r is the amount of time it takes to grow or double in size. you could also switch the two to whatever the rate is like in this equation it is 420/100 per hour. so 100(4.2)^(t/1 hour)
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. (2)
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.
@ 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...
I have watched some of your videos, but I still don't understand what k actually means. In my textbook, it says that k is the relative growth rate and k is used in the equation A(t) = Ae^kt. I know how to calculate the k. However, if I am asked to find the relative growth rate, I will first divide 420 by 100 and say that the rate exactly equals 4.2 and that is the k. but why I need ln(4.2) = 1.435 = k, it doesn't make sense if the growth rate is 1.435. can you explain their difference, please
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!!!
![เป็นไปได้ไหม - WanMai [Official MV]](http://i.ytimg.com/vi/_6lZ6b3_7Vo/mqdefault.jpg)
Who else was thinking when the phone rang, "Better call Sal"?
Please somebody redesign the tablet to be able to function with improvement multitasking hardware?love math math indeed.1/501=
I love you. This is the best form of charity (that helps me). Thank you
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.
A very good problem in exponential growth.
Thank you
@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!
makes more sense to use b(t)= I(2())^(t/r)
where r is the amount of time it takes to grow or double in size. you could also switch the two to whatever the rate is like in this equation it is 420/100 per hour. so 100(4.2)^(t/1 hour)
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.
(2)
isn't it geometrical progression?
You are AWESOME. I am starting to like Calculus because of you. Thank you!!!!!!!!
Thanks man, I had to learn this for biology at UCSD and even the professor couldn't explain it as well as you did.
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.
@ 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...
y=a * b^x
Final = Initial x Growthrate^time
growthrate = x√Final/Initial
unknown final = Initial x knowngrowthrate^x
Helped a lot. You are the best!!!!
omg i just noticed i can make exponents with ctrl + alt
for example 2²
doesn't work in my computer
Nice :) can't do that on mobile though :(
THIS IS THE SAME EXACT QUESTION ON MY HOMEWORK XD... coincidence? I think not!
Calculus Early Transcendentals, 7th edition, Exercise 3.8.3? :p
yes! XP
That's neat :D
exponential decay? Have you developed a mathematical expression for describing the imminent loss of penicillin?
It's the Euler Number (For natural growth). It's an infinite number just like Pi, look it up on wikipedia ;).
Where did the e^kt come from? Is there a formula for expo growth that i am not aware of?
AGh You scared me. I forgot This window was open when it started playing.
How do you solve a problem like this if you do not know how much bacteria you start with?
This is the exact same problem ( problem 3) i was looking at in my book, Early Transcendentals
great video i learned alot
b(t)=100(4.2)^t
Wouldn't this be a simpler form of the expression for the number of bacteria after t hours?
this is the exact problem in my book chapter 7.3 #3 lol thank you i needed help on c
Whats the name of the book?
luvv ur vids!!
i think i understand more from here than from my actual teacher sometimes
[haha phone from dish network :P]
Where does the "e" come from? Is it mandatory???
I have watched some of your videos, but I still don't understand what k actually means. In my textbook, it says that k is the relative growth rate and k is used in the equation A(t) = Ae^kt. I know how to calculate the k. However, if I am asked to find the relative growth rate, I will first divide 420 by 100 and say that the rate exactly equals 4.2 and that is the k. but why I need ln(4.2) = 1.435 = k, it doesn't make sense if the growth rate is 1.435. can you explain their difference, please
I think you should redo this problem. It was very messy, pixelated and all over the place. I had to rewind the video because I lost focus.
there is a subliminal message in the first problem ;D
Thanks for the help
That's pretty neat ;)
Answers (b) 7406, (c) 10591.8, (d) 3.22 hours
this guy likes the sound of his own voice way too fucking much
thank you sooo much! this helped a lot!
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!!!
the way you do it in the states is alittle different than that of nova scotia
What do you do if you end up with a fraction as k? Like it's ln(87.14/101.3)/3000? We can't use calculators.
you dont hav to use product rule when you mutilply 100e^ln....?
thanx one more time... im taking algebra 2
hahah the phone that was brilliant! ur the best!
How did you go from e^k=4.2 to K=ln(4.2)
When you take the natural log of both sides, the e goes away, leaving the exponent (k) and then the other side is ln(4.2)
use hippo campus .org, they are the same videos without the annoying comments or ads.
do you have any specific answer?
"The population has increased to $4.20" haha @15:28
Thanks Sal
420 and rasta colors, i think he's trying to tell us something...
420??? thats the devils number!? :O.great vid besides that though
There is no place for superstition in mathematics.
666
?? 666 is not 420 lol
thank you, it helped a lot
I think he needs to give a more intuition on how e^ln4.2 works.
thanks!
I think it would be much easier to understand if you used b(t) = ia^t, rather than b(t) = ie^(kt).
yes it would
And yet here you are listening to it. Someone likes making stupid comments way too much.
someone buy this guy a calculator
sorry I didn't notice you got it. anyhow, i got to play smart :P
First of all, what is the proof of this formula?
12 people are public school teachers
i dont get it
Did you watch the whole video?
Our school does y= bg^x
same, it's also called geometrical progression
omg this is the exact same problem in my book that i came to look at this video for
skipped steps and messy hard to follow
haha, you must have a high tolerance for people wasting your time then
420
please buy a calculator
lol
terrible hand writing software
I don't agree at all... I don't think you have a good idea of what this person is like.