Exponential Decay

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  • @evgeniibarannik8996
    @evgeniibarannik8996 Рік тому +35

    "Exponential decay occurs throughout physics and engineering ..."
    Well, I wouldn't call our situation all that bad. At least we have your videos 😊

  • @ManyHeavens42
    @ManyHeavens42 Рік тому +14

    It will take considerable time to wrap my head around this, this is invaluable sence all we have is time.

  • @panupentikainen953
    @panupentikainen953 Рік тому +13

    Every video you make is a gem. Thank you!

  • @sebastianweissbarth3385
    @sebastianweissbarth3385 Рік тому +8

    Such an elegant Mathematical analysis of Zenos paradox! A gem!

  • @nathank7569
    @nathank7569 Рік тому +6

    A good follow up to this would be expanding on underdamped, critically damped, and overdamped responses in physical systems, which are the real tools used across many disciplines to explain just about everything.

  • @physicslover1950
    @physicslover1950 Рік тому +21

    My mentor! This is the best ever intuitive video about exponential decay that I have even seen... I loved the way you brilliantly made the use of cokors in your equations of black and red curve..
    This is the thing which you and only you made me memorize in 12 mins which I couldn't even memorise in 45min if I were using a book.. Thanks to your smart work.
    I also find a lot of difficulty in making the differential equations that describe the behavior of physical systems.. I am good at solving differential equations but I am really bad at making differential equations... Will you please make a video on the easiest way to make a differential equation for any system.. I would be very thankful to you and my happiness will know no bounds if you make this in future.. 🌹🌹🌹💐💐

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +12

      Thanks for the compliments. Differential equations are on my list of topics for future videos.

  • @gregorymccoy6797
    @gregorymccoy6797 Рік тому +5

    Love it. This was the equation (or at least a form of it) we used in school for capacitor/inductor charge when predicting pulse wave forms.

  • @adolf_08
    @adolf_08 Рік тому +12

    I have learned a lot with each of your videos, thank you :)

  • @kartikg.kartikg
    @kartikg.kartikg Рік тому +2

    Your videos are making me understand the topics exponentially.
    You are the best.

  • @Turtle1967A
    @Turtle1967A Рік тому +4

    I am always happy when I see Eugene has released a new video :)

  • @Henrrrrrrrrrryyyyyyyyyyyyyy
    @Henrrrrrrrrrryyyyyyyyyyyyyy Рік тому +3

    p.s. the exponential isn’t coming from nowhere. It often comes from simple ODEs

  • @user-kx2kw7uc2v
    @user-kx2kw7uc2v Рік тому +1

    thanks!Best knowledge and good music...it is wonderful

  • @anirudhkolli2241
    @anirudhkolli2241 Рік тому +6

    Thank you, I have learned a lot from these videos!

  • @BushCampingTools
    @BushCampingTools Рік тому

    Love the car number plate! But seriously, great video and great explanation! Plus love the worldly advice too LOL, so true!

  • @fahimahmedbhuiyan2252
    @fahimahmedbhuiyan2252 Рік тому

    Your videos literally make me happy and whenever I see your new videos, I just dive in right away ❤!

  • @emin_akdas1
    @emin_akdas1 Рік тому +2

    I am happy like a child's curiosity is satisfied while watching your videos. You add perspective on the universe and its foundations. I understand mathematical expressions better by turning them into images in my mind. All I need to learn is an explanation from someone like you.

  • @mikkel715
    @mikkel715 Рік тому

    Exponential Decay seems to correspond well for us software developers..
    Super to see a new video here.

  • @52flyingbicycles
    @52flyingbicycles Рік тому +1

    2:40 you just called out the entire business sector right there

  • @ViciousViscount
    @ViciousViscount Рік тому

    Oh boy, did I miss this beautiful voice and the unsettling animations.

  • @y5mgisi
    @y5mgisi Рік тому

    Love the videos on this channel.

  • @pedrovelazquez138
    @pedrovelazquez138 Рік тому

    Greetings from Paraguay. I follow your work since 2014. Great content, it is unvaluable.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      Thanks for the compliment about my videos. I am glad that you like them.

  • @morkovija
    @morkovija Рік тому +1

    Perfect soundtrack for the subject, thank you

  • @murtadhamaythamalbahadily7973

    Thank you very much ❤️ for your great educational videos and your compassion (vegan for animals).

  • @alamagordoingordo3047
    @alamagordoingordo3047 Рік тому +1

    Beautiful video excellent explanation. Thank you.

  • @TheMrFiletofish1
    @TheMrFiletofish1 Рік тому

    Awesome video, my favorite channel for years now

  • @guilhermerafaelzimermann4196
    @guilhermerafaelzimermann4196 2 місяці тому

    2:41 was brutal yet honest, that is pretty much what happens with so many bussineses

  • @jlpsinde
    @jlpsinde Рік тому +1

    Amazing, love this

  • @sahzamirfatemi3673
    @sahzamirfatemi3673 Рік тому +1

    Thank you
    I am following you from Afghanistan.

  • @Tim-Kaa
    @Tim-Kaa Рік тому

    Love your vids.

  • @LuisAldamiz
    @LuisAldamiz Рік тому +1

    And that's why, kids, Achilles the Swift was beaten by a turtle: exponential decay, alias Achilles' sophistry curse.
    Honestly I was sorta disappointed by the car going ever slower example, something that doesn't really happen in real life. Still an interesting issue in terms of fundamental physics.

  • @smit1909
    @smit1909 Рік тому +1

    Your all videos bro best 👍👏

  • @jasminemallick1215
    @jasminemallick1215 Рік тому

    Man your content deserves millions of views and subscribers

  • @squaremarket973
    @squaremarket973 Рік тому +2

    Zeno's paradox-ish

  • @jmegawarne
    @jmegawarne Рік тому

    That stab at continuous improvement though.

  • @larryyonce
    @larryyonce Рік тому

    Brilliant !

  • @zacharywong483
    @zacharywong483 Рік тому

    Excellent explanation!

  • @pantherplatform
    @pantherplatform Рік тому

    I love this channel

  • @aaronwong2773
    @aaronwong2773 Рік тому

    Thanks. Your video made me think a lot. t->endless means never stop. Keep simple. Keep kind. Keep share. t->endless We are infinitely close to the truth. Bro Never Stop.

  • @deslomeslager
    @deslomeslager Рік тому

    I have learned on school that a capacitor may be seen as 'full' after 5 Tau (or empty when discharging). Always good to draw a line on infinite functions.

  • @satvikvarun6386
    @satvikvarun6386 Рік тому +2

    First view and like❤️

  • @zyroxiot9417
    @zyroxiot9417 Рік тому

    Great, 👍🏼

  • @AnthonyZboralski
    @AnthonyZboralski Рік тому

    Many thanks! It puts a smile on my face every time you release a new video. Where are you based?

  • @sanket__bharti
    @sanket__bharti Рік тому

    very good explanation
    Love from India

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +1

      Thanks. I am glad you liked my explanation.

    • @sanket__bharti
      @sanket__bharti Рік тому

      @@EugeneKhutoryansky event i should be thanks for giving a good visual explanation

  • @adityachauhan7016
    @adityachauhan7016 Рік тому +1

    👍👍👍👍

  • @mustafizrahman2822
    @mustafizrahman2822 Рік тому

    Love from Bangladesh

  • @Downlead
    @Downlead Рік тому

    A new video... 👍🏻

  • @gowrissshanker9109
    @gowrissshanker9109 Рік тому

    Hlo Eugene, How come the position and momentum are independent variables in Hamiltonian mechanics? Consider SHM Hamiltonian when we change position , Momentum changes right?
    Both are related to each other right?
    Thank you

  • @Khalid-Ibn-Al-Walid
    @Khalid-Ibn-Al-Walid Рік тому

    Hello Mr khutoryansky, I've just Ended high school, your videos are helping me a lot, especially in understanding what lies "behind the formulas" and also in visualising or confirming some of my visualizations of some phenomena, physics are really not the same in school, many students and teachers just learn everything even formulas ( for example I'm studying the atom structure now, teachers only want us to learn the formulas by heart ( number of electrons in a shell 2n², in a sub shell 2(2l+1) and stuff like that, especially for klechlowsky rule, I still struggle to understand from where it comes only taking consideration interactions between charges, but they only asked us to learn by heart) ... if animation like yours where used in teaching I'm sure it would really bring great benefit, it's better to fully visualise and understand with an intuitive way 10 phenomena than learning 50 formulas.
    The thing is to explain EVERYTHING starting without admitting anything starting from only 2 things:
    A mass attracts another mass
    Positive and negative charge attract each other, the same charges reject each other.
    With these two we can explain all the physics, all the phenomena should be explaining starting from these 2 rules and then start building with logic, it would be so great if in high schools or universities all the phenomena were explained beggining from these 2 principles and building progressively as you do...
    Anyway, thank you very much for all the efforts you are doing , you help a lot !!!

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      Thanks for the compliments and I am glad that my videos have been helpful. What you describe is a very common problem in science and math education. If you haven't seen it already, I actually have a video where I talk about this titled "How not to teach physics" at ua-cam.com/video/k6QhhocnZ-M/v-deo.html

    • @Khalid-Ibn-Al-Walid
      @Khalid-Ibn-Al-Walid Рік тому

      @@EugeneKhutoryansky Thank you very much for the video ! This is clearly descrining what I was thinking at, you showed really well what was the problem with nowadays education system. hope the situation will change and that some "official institutions" may finally understand that the real understanding of science's cannot be made only by the use complex mathematical formulas, but by visualisation as you said in the video. I think that if this (visualisation of phenomena and their intuitive/logic explanation ) was taken as a priority by high institutions, it will really change the course of the evolution of engineering (inventions), because new concept idea never come from looking into mathematical formulas and variables rather new inventions come from the visualisation of phenomena that allows to imagine lot of new scenarios where we modify some parameters of the phenomena.
      Btw thanks again for sharing these exellent videos ! For the moment I find your channel to be the best one for visualizing phenomena, understanding them and especially in explaining everything step by step ( I mean without admitting formulas or principle, rather by explaining them)

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      Thanks!

  • @TheJonathanNewton
    @TheJonathanNewton Рік тому

    Exponential decay is what I see in the mirror every morning.

  • @peaceling9826
    @peaceling9826 Рік тому

  • @amaneyuuki6569
    @amaneyuuki6569 Рік тому

    This video looks nice but it could be better if you added some explanation on how those physical systems behave like that. Mathematically, this means the rate of losing something is proportional to the current amount.
    For the electrical examples, you can take the instantaneous potential difference, current, electromotive force, etc. to show the aforementioned relationship.
    For the radioactive decay, maybe this deserves another video. It's an interesting topic because instead explaining the exponential decay, we can use the observation to understand more about it. The exponential decay shows its spontaneous nature, especially the aspect of "no build up". To understand that, you should look at what "with build up" looks like.
    Let's say we have some houses, built in the same way, stay in similar conditions, and they "randomly" get damage over time. It's not actually the same "randomness" as radioactive decay, but still "random" in the sense of we can't exactly predict it. If you see 2 houses standing, you see no apparent difference, and you are provided the fact that one of them was built 10 years earlier than the other; then which house do you expect to collapse first (if both of them are left unattended)? Reasonably, the older house is likely to collapse first, because even if we can't see any apparent damage, there can be damage built up inside. The probability of "still standing" of one of those houses over time is NOT in the form of exponential decay.
    It's different for radioactive materials. We can observe a radioactive material from its creation. Let's say:
    - in day 1, we take 10 billions radioactive atoms created in day 1 to put them in the first box;
    - by day 2 there were 1 billion of them left in the first box;
    - also by day 2, we take 1 billion radioactive atoms of the same type created in day 2 to put those new atoms in the second box.
    By day 3, which box do you expect to have fewer radioactive atoms? Is that the first box because there are likely unobservable built up damage/instability in the atoms in the first box? The experimental answer is that those two boxes have the same expected rate of decay (they may not be exactly the same, but the probability of one being more than the other is the same as vice versa, just like counting the times of head and tail when tossing a coin for many times). This predicts there is no "built up damage/instability".
    You may think of "no built up damage" as for every minute, you toss a dice, if the dice lands 1 then you break a box, otherwise the box is left intact. But this would suggest a basic period. And so far we can't find such basic period for radioactive atoms (if such basic period exists, it would have very short time for each period).
    In quantum mechanics, we calculate/explain it as the wave function for all "haven't decay", "decay at t_1", "decay at t_2",...(with infinite and continuous list of moments in time) just exist together. By Copenhagen interpretation, when you observe them, they collapse into a particular case, for example: "decay at t_2", and other cases cease to exist. By multi - world interpretation, there are many world with many "you" observing the radioactive atoms, with each of "you" being able to interact with only one matching case, not the others; for example the "you" of "this world" can only interact with the products of the case of "decay at t_2", not the yet-to-decay atom in another world (which can be observed by the "you" in that world).
    Side note: editted to use more accurate words.

  • @peopleicat115
    @peopleicat115 Рік тому

    Very god pozitif bms movi batary neew movi ples very good movi thenk you

  • @KaranSuman
    @KaranSuman Рік тому +1

    Please, consider having a 'Thanks' button under your videos. That way anyone can donate to you with ease.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +1

      I have never heard of this before. I will look into it.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +1

      By the way, I already have a Patreon page where people can donate. The link is on my UA-cam home page.

    • @KaranSuman
      @KaranSuman Рік тому +1

      @@EugeneKhutoryansky Yes, I know that you have a Patreon page. However, aren't two ways to donate better than only one?
      The feature I am talking about is known as Super Thanks. Please, consider taking benefit of it.

  • @shatterthemirror8563
    @shatterthemirror8563 Рік тому

    How do you reach your goal if you can only walk halfway there in equal time intervals?
    So first you will need a pair o' Docs.

  • @cuteworld8056
    @cuteworld8056 Рік тому

    Thank you sir

  • @shawnmcgrath299
    @shawnmcgrath299 Рік тому

    moores law just hit my brain

  • @user-kr3ct9oh4y
    @user-kr3ct9oh4y Рік тому

    0:30 Vegan for animals. Love you!

  • @TheRolemodel1337
    @TheRolemodel1337 Рік тому

    in the 7th or 8th grade when we dealt with exponential functions i had the thought of halving the speed of a car until it stops and realized it will never stop if space is infinitely divisible so this sparked some physics questions about the nature of motion which my physics teacher couldnt resolve 😅

    • @jmchez
      @jmchez Рік тому +5

      That's just a version of Zeno's arrow paradox, which Aristtole thought was absurd and, which Isaac Newton solved by explain it with calculus. In the real world, you would reach a distance of one atom and, there, Heisenberg's uncertainty principle makes the "How far are you?" a moot point.

  • @casehuae8109
    @casehuae8109 Рік тому

    Hello , is this animation also made with Anime Studio? I would like to do a similar demo video , too. At the same time, I want to ask you how to get started with this kind of animation production.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      My 3D animations are made with "Poser." I have a video where I explain how I make my 3D animations at ua-cam.com/video/6Hl5dvA88Uo/v-deo.html

    • @casehuae8109
      @casehuae8109 Рік тому

      Wow! thank you so much . 😘😘😘😘@@EugeneKhutoryansky

  • @beinghimself
    @beinghimself Рік тому

    You could’ve explained more the idea that exponential means: changes with a fixed proportion to the current quantity. So it doesn’t care about anything else. If we take cells proliferating, you would have one cell then two then four then eight. You can see that the bigger the number the bigger the speed of proliferation (cells produced per second), and if you double the cells you double the speed (from 4 to 8, now i go twice faster meaning from 8 tp 16) so V=kN with v as the speed of proliferation and N the number of cells or let’s say dN/dt= kN. You can see that dN/N = kdt is fixed for a certain time interval. And that’s the idea. Then you could write N= No/e^(t-to/tao). and the time that has passed compared to the time constant determines the decay, so a t-to that is equal to ln2*tao would make the exponential e^(ln2) and thus you’re dividing by 2. If equal to aln2*tao then e^(aln2) thus you’re dividing a times by 2 and the ln2*tao is what we call t1/2 half life, but you don’t have to include this in the video am just adding information. An atmospheric pressure is also decreasing exponentially for example. It’s because it decreases with a fixed amount compared to what it has. That’s why we find the exponential function more than other functions in nature (it makes sense, and it gives you the change per change in time no matter how big it is. It tells you look, after a fixed amount of time or distance, you change by half of what you have, wait the same time or distance, it changes by half what you have. Try to understand these ideas but of course it’s just a comment i can’t provide a clearer explanation

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +1

      I address this in more detail in my video on exponential growth at ua-cam.com/video/Vqc1M1agKgA/v-deo.html

  • @pieduacademy219
    @pieduacademy219 Рік тому

    How to you create your videos and what tools du u using for videos??

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      I explain how I make my 3D animations in my video at ua-cam.com/video/6Hl5dvA88Uo/v-deo.html

  • @lol51000
    @lol51000 Рік тому

    What if what we call "physical constants" are in fact variables that grow slowly toward their actual values? And so slowly that we consider them constants?
    Would it be possible that the speed of light change through time? And maybe explain things like what we call dark matter?

    • @SplendidKunoichi
      @SplendidKunoichi Рік тому

      if what we call light ever changed it's speed, i'd mostly be concerned with how any possible changes in what we call speed could've been ruled out first..

  • @aquagardenalgae2833
    @aquagardenalgae2833 Рік тому

    I used your differential for such control and borrowed the idea from you, but its implementation requires a lot of effort...

  • @granhermon2
    @granhermon2 Рік тому

    Bienvenidos a reduzca!

  • @CAPSLOCKPUNDIT
    @CAPSLOCKPUNDIT Рік тому

    Zeno enters the chat at 0:30.

  • @leewilliam3417
    @leewilliam3417 7 місяців тому

    Mmmm😊

  • @BariumCobaltNitrog3n
    @BariumCobaltNitrog3n Рік тому

    Infinity as a number seems a little sketchy. What is infinity -1? Or is it just turtles all the way down?

  • @JuliusUnique
    @JuliusUnique Рік тому +3

    10:30 if a particle is 0.5 it means 50% of the time the whole particle is there

  • @peopleicat115
    @peopleicat115 Рік тому

    Pozitif kurrent batary movi ples thenk you

  • @SachinSingh-pu1nc
    @SachinSingh-pu1nc Рік тому +1

    Effect of biological stimulus is another example.

  • @davebennett5069
    @davebennett5069 Рік тому

    Zeno's mini cooper?

  • @Adam-ox6zy
    @Adam-ox6zy 15 днів тому

    Plot out all the ages of the main characters given in the bible from the time post flood and guess what? You get an exponential decay curve.
    Now either the authors knew about this law (highly unlikely) or the authors were describing what they saw, which is much more likely.

  • @Petrov3434
    @Petrov3434 Рік тому +1

    It would have been great if you started with definition of exponential…

  • @physicsbutawesome
    @physicsbutawesome Рік тому

    Nice, I like the last couple minutes where you move away from the purely mathematical formulation and talk about how the concept is applied to real situations.
    I think this is the most important bit with things like this, sure the mathematical properties are interesting, but how do they apply to actual particles or objects...

  • @DavidG2P
    @DavidG2P Рік тому

    Can you make a video about exponential radioactive decay? Allegedly, radioactive decay of ONE particle is "indeterministic" and totally random. Still, half-life time is EXACTLY determined (and different) for every material. Something must be wrong with quantum physics here.

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому

      There is nothing wrong with quantum physics here. This is just the "Law of Large Numbers." I cover this in my video "Probability - Quantum and Classical" at ua-cam.com/video/X2eomv6XfWo/v-deo.html

  • @bruceshowalter6046
    @bruceshowalter6046 Рік тому

    Zero entropy = ♾ negentropy

  • @josesandoval4381
    @josesandoval4381 Рік тому

    Quien lo tradusca al español se ganará las gracias y miles de like.

  • @jonathandelapaz6436
    @jonathandelapaz6436 Рік тому

    Shout out to the Jojo fans out there who get this

  • @roshan0405
    @roshan0405 Рік тому +1

    Where are you from?

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +4

      I was born in the Soviet Union, but I have lived in the United States since I was four years old.

  • @hindswraj4883
    @hindswraj4883 Рік тому

    Software use for these type of animination

  • @pantherplatform
    @pantherplatform Рік тому

    Reminds me of the half life of prescription drugs...

  • @CannabinatedFantasy
    @CannabinatedFantasy Рік тому +1

    2:45 @ obama

  • @etherealpizza
    @etherealpizza Рік тому

    Is e Euler's constant or am I missing something

    • @EugeneKhutoryansky
      @EugeneKhutoryansky  Рік тому +3

      It is Euler's number. Euler's constant is not the same thing as Euler's number.

    • @etherealpizza
      @etherealpizza Рік тому

      @@EugeneKhutoryansky thank you

  • @yksnincini3747
    @yksnincini3747 Рік тому

    Videolarınıza lütfen Türkçe çeviri altyazısı katın

  • @sleepn_on_me2473
    @sleepn_on_me2473 Рік тому

    Im tripping balls…..

  • @peopleicat115
    @peopleicat115 Рік тому +1

    Batary movi ples

  • @saqibraza1083
    @saqibraza1083 Рік тому

    Mam, please gave response to my mail....I'm confusing about one question so please help me.

  • @ed.puckett
    @ed.puckett Рік тому

    The analogy to "continuous improvement" isexcellent

  • @amv6875
    @amv6875 Рік тому

    Finally

  • @reoproedros
    @reoproedros Рік тому

    is time the anti-matter ?

    • @jareknowak8712
      @jareknowak8712 Рік тому

      No.
      Time is a dimension.
      A-M is a type of physical object.

    • @reoproedros
      @reoproedros Рік тому

      @@jareknowak8712 if there is something like anti-matter , why should it be positioned in space , like matter is ?

    • @jareknowak8712
      @jareknowak8712 Рік тому +1

      @@reoproedros
      For example - we can produce a tiny amount of AM in CERN, and CERN is located in space-time.
      The difference bt "normal" matter and AM is the opposite sign of electric charge and differencies is quantum numbers. AM have the same mass.

    • @reoproedros
      @reoproedros Рік тому

      @@jareknowak8712 thank you . i have to read more to catch up

  • @PeterPan-vt6sy
    @PeterPan-vt6sy Рік тому

    I wonder if this is how reincarnation works. Our souls are “decaying” but never reaching the end since it’s “eternal” each time we reach half of the journey we die and are reborn. Take my comment with a grain of salt I just like to see metaphors with the physical and spiritual

    • @PeterPan-vt6sy
      @PeterPan-vt6sy Рік тому

      If you look at the diagrams it could almost be made to look like a double Helix. I wonder if there’s undiscovered math that humans could find out in the future to possibly reverse entropy

  • @alanlihic
    @alanlihic Рік тому

    Man this video IS your "continuous improvement" idea you say we should mistrust, it's so boring and so long! And it brings nothing, the exponential decay is a classic.

  • @lMINERl
    @lMINERl Рік тому

    Disliked i dont see any red arrows while riding a car