Added: 4 years ago
From: wonderingmind42
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  • Thanks for uploading!

  • Thanks so much wonderingmind42. Real education.

  • i just googled vail ski lift prices, $111.... close but would have to go up 49 bux next year.... im english and chedder is a great cheese

  • @deadeyedavies Shit... the price of ski lift tickets debunks his entire lecture! Quack! Fraud!  Fear-Monger! ;) j/k, mate!

  • fantastic video.

  • all i took out of that was

    the number 7 sucks

    wheat grows

    and that i need some electricity at some point

  • is this guy speaking English

  • i think the greatest shortcoming of man is the perception of self

  • @imapisces23 amen

  • all hail the new chuck norris !!!!

  • @MsFootballunited he chuck norris'd my brain

  • why's the Texas Ranger explaining exponentials?

  • it this is the most important video I will ever see I better shoot myself... or become an eternal academic and thus... shoot myself

  • Thumbs up if you checked the current price of Vail ticket in Google

  • 4 million views?! Must be because he looks like Larry David in the thumbnail.

  • Excellent! People need to know what they are getting into when they take out loans. In England children used to be told the mythical story about re-shoeing a horse in the olden days. The rider accepted the quote of a farthing for the first nail, a halfpenny for the second nail and so on. Even if there were only five nails per shoe the bill would be enormous, £1092 approximately as the old pennies were 240 to the pound. The video is a bit Malthusian but there is nothing wrong with the maths!

  • @137P0359997,I disagree, go to thunderbolts.info search for abiotic oil and join the debate. 

  • I guess king hanged the chessman

  • you do realise the music for this is based on the Cminor prelude Bk1 by bach!

  • Someone should have told him oil is abiotic :/. It's sad he wasted so much time on the oil subject. Everyone should know by now oil is Not from dinosaurs.

  • @livnthadream25 Petroleum is mostly from plankton and algae. Therefore biotic. This is proven for all known deposits.

  • @livnthadream25 Everyone should know by now? This lecture looks pretty old lol

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  • Nobody's taking notes haha.

  • THIS IS NOT IMPORTANT! THIS CAN SUCK!

  • Comment removed

  • the white Morgan Freeman

  • Those 12,000 people who have upvoted this video scare me. So much idiocy on Earth. Most of this 10-minute video is dedicated to explanations and demonizations of the exponential function. Don't you know it from the basic school? Don't you understand it's just a function and there's nothing scary about it?

  • @lumajs It's basic - but that is the point. It is basic and simple and not grasped by about 90% of people. Most economists, for example, are enslaved to the concept of never ending growth.

  • @garethb1961 Dear gareth, the exponential growth has to cease in some situations (although, sometimes, after many decades) but it may continue indefinitely in others. For example, our Universe will become an exponentially growing de Sitter space (forever). In the same way, economists are right that GDP counted in the money may grow indefinitely, too.

  • @lumajs If one tried to link the GDP to the mass of coal on Earth, clearly there would be an upper limit on the GDP given by the mass of coal on Earth. However, the structure of the income is changing as various things are getting cheaper and new products to be bought emerge. Even when inflation is subtracted, the real growth rate may be positive (3%) forever. There's no contradiction here.

  • We are told that they can not pay a living wage and workers have to live off Minimum wage so they can have 5-10 big big homes, all the cars they ever want the best health care yada yada yada.

    Workers have to suffer so they can live so well.

    It is clear they can not manage resources and the state has to take over all business activities now.

    All profits goes to the state, benefiting all workers and citizens.

    We do not need evil greedy rich anymore. they serve no purpose.

  • @MrAppleseed88 You're insane.

  • WE ARE UNDER THE CONTROL OF AN EMPEROR; BUT UNLIKE A NORMAL EMPIRE THE EMPEROR REMAINS IN THE DARKNESS, HE DOES NOT REVEAL HIMSELF TO THE PEOPLE.

    BUT HE ACTS THROUGH EMISSARIES, FIRSTLY THE BANKING SYSTEM WHO CREATES THE MONEY, THEN BIG COMPANIES WHO USES THE MONEY, AND THE MEDIA AND THE POLITICS WHO IS PAID TO KEEP THE PEOPLE IGNORANT AND STUPID, THE MILITARY TO REPRESS THE REBELLIONS AND TO EXPAND HIS DOMINATION. THEREFORE IF YOU WANT TO BE FREE AND INDEPENDENT THE WAY IS THE REVOLUTION!

  • @BrAiNs102 Just imagine it is BETTY WHITE.

  • @BrAiNs102 And we KNOW thats what YouTube is REALLY for.

  • Stupidly grandiose titles like "the most IMPORTANT vid you'll ever see!!!" immediately give me the shits... but then again, compared to the crap I usually watch on youtube, it probably isn't far off.

  • this is music to my ears

  • Yawn....

  • It boggles my mind that after 12 years of school there would be anyone who didn't know this stuff. There is also a saying, "Tree's don't grow to the sky".

    By the way, that 70 math he talks about? It is usually called the "Rule of 72" for obvious reasons.

  • I know and believe that the exponential function is imperative, but as a human being, I also realize that the variables are always shifting, and the base is continually changing. Nuclear power is the doomsday device, based on the details left out of that equation, some say.

  • There is an awesome Facebook fan page named "Irony: Overpopulation could lead to human extinction."

    Thank you so much for this video.

  • Oh, and the next mother f'cker to use the words Ron Paul "Idiots", i will get your IP address, hunt you down and cut your kidneys out for use on the medical black market. If you don't understand Ron Paul nor what he stands for, you my friend are the complete and unevolved master IDIOT. You missed the bus BIG TIME!

  • @greezy39 You are just another Ron Paul idiot - get over it

  • almost 4,000,000 views and only 13,000 ratings. Looks like a lot of disinterest to me, for the supposedly "MOST IMPORTANT VIDEO YOU'LL EVER SEE". Stop manipulating mine and everyone else's interest with epic titles like that you A hole.

  • @greezy39 nononononononon most viewers dont have a youtube accoutn so they cant vote

  • @greezy39 Some videos on youtube have only few thousand views and they are better than videos with milions of views.

  • bolo tie

    

  • who cares?

  • Very interestin',...thumbs up and you're wrong here Wonderingmind42, no boring vid here!!

  • With more humans, the knowledge base grows exponentially and human ingenuity keeps growing our ability to do new things that couldn’t be done before. Its funny as the population here keeps growing so does our ability to create more energy and more food, while at the same time our air and water is cleaner. Humans can create a building on top of an acre of land that creates thousands of acres in its place. We will build space craft to explore the universe.

  • there's one thing i don't get. assuming we have a growth rate of 100% per year. the doubling time is 70 divided by 100 which equals 0,7 years. this obviously contradicts the fact that a growth rate of 100% means doubling every year, not every 0,7 years.

  • @centionnes Population Growth Rate (PGR) is NOT measured as yearly discrete growth rate but continuous compounded growth rate. The time interval is not one year but infinitesimal. Just as in nuclear decay, if you have read that. When growth/interest is compounded and time period is small, things grow much rapidly as opposed to simple interest (something you are thinking of).

    See: en . wikipedia . org / wiki / Population_growth#Population_g­rowth_rate

    (remove white spaces from the above link)

  • No Professor Bartlett, the greatest shortcoming of the human race is not "our inability to understand the exponential function" but rather, it is sin and rebellion against a perfect, righteous, and holy God. Sin is what caused ALL problems on earth including death.

  • @ToshiroHoshi Religion is the source of all wicked actions in the world. Good people do the best they can. Bad people do the worst. BUT, if you want something REALLY WICKED, it requires a Religion, based on one of the many thousands of INVENTED gods over time. You are an Atheist with regard to all but 3 gods if xtian, 2 gods if jewish, and 1 if islamic. The only TRUE monotheism is the worst one, islam.

  • @somthinjustaintright It's understandable that some would think that since people have twisted and perverted the truth for their own selfish ends. Study Jesus Christ Himself. He said, "Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me." John 14:6. Don't judge truth by the failure its/His "followers".

     As far as monotheism, no, the Trinity is true monotheism but it's a reality that exists outside of space and time.

  • @ToshiroHoshi I was a cradle raised Roman Catholic, educated by the Schools Sisters of Notre Dame and The Society Of Jesus,aka,Jesuits. Don't presume to preach Dogma if you do not know what it is

  • what?

  • My previous post got garbled. F is future P is present, r is growth in percent ^ power op n is years F = P (1 + r) ^ n Now, we are interested in a doubling, and so F = 2P (double of the present value) 2P = P (1 + r) ^ n 2 = (1 + r) ^ n Taking natural logs on both sides ln 2 = n ln (1+r) When r is small, ln (1+r) can be simplified to r 0.69 = n r 69 = n (100r) 69 = nR Using 70 (as the Professor does in the video) allows us to quickly say that when R=7, n=10. When R is 5, n=14 etc.
  • It's actually quite easy to derive from basic mathematics. F = P (1 + r) ^ n Now, we are interested in a doubling, and so F = 2P (double of the present value) 2P = P (1 + r) ^ n 2 = (1 + r) ^ n Taking natural logs on both sides ln 2 = n ln (1+r) When r is small, ln (1+r) can be simplified to r 0.69 = n r 69 = n (100r) 69 = nR Using 70 (as the Professor does in the video) allows us to quickly say that when R=7, n=10. When R is 5, n=14 etc. QED
  • So the doubling time of a 100% growth rate per year is 70/100 = .7 years? That doesn't make any sense. Could someone explain this to me.

  • @linkdead14 yeah, that would actually be right. If you are compounding daily, remember, you will actually reach 100% faster than one year. That's why the annual yield is always higher than the APR.

  • BIGFOOT

  • 666 dislikes :)

  • This is pretty basic stuff that I learned in school years ago.

  • @PhoenixShadow57 I think the difference is that in the ten year model, growth is calculated exponentially.

    If it was seven percent of the initial number per year for ten years it would be the same as seventy percent. However, the growth in any given year is greater than the growth of the previous year because it is seven percent of the previous year, not seven percent of the first year.

    That is the small distinction that makes the huge difference. That is how I understand it, anyway

  • This video is so important, i'm going to make a giant monument in memory of this video with a Giant Red Square with rounded edges that are lined in silk and in the center it will have a play button

  • this is still the best video so far, and lead me to learn/ understand that science publication is not always true. thanks you.

    if you want to know why here it is. search

    Lec 22 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008

  • @callmejon start at 37:34 Lec 22 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008

  • this music is based on the Prelude from the first book of 48 preludes and fugues by bach no.2 in c minor!

  • Let me break this down for you: what you use to pay for a home is now the cost for an automobile. I just saved you 4 hours. You're welcome.

  • THis is such bullshit. what the hell lol

  • Don't waste your time on watching these videos, this man is a buffoon. He actually believes that the population can go on increasing to infinity. Populations don't rise exponentially, but logistically. There is a little something called "carrying capacity". People just can't go on reproducing forever. Math standards really were lax back then.

  • @TagRation He mentions the inevitability of zero population growth. Think of how fucked you'd be if you weren't one of the very rich.

  • @TagRation dont worry the goverment is stimulating this generation not to reproduce, ooh didnt we tell you if you dont have population growth the money system doesnt work whwhaaha lol, it doesnt matter if the population growth is the problem if that isnt then it is that population growth cannot keep up with the capitalistic system(based on %)

  • @TagRation "There is a little something called "carrying capacity""

    Then you should understand that in nature population increase dont stop magically after reaching carrying capacity but after overshooting it.

    And you should also know what effects of overshooting it are.

  • I found this cool actually,I never understood what the number e was about.

  • I just don't get the doubling time thing, if we have something for example that is at a growth rate of 70% a year, it wouldn't take 1 year to double it would be a little more....

    can someone please explain?

  • @PhoenixShadow57

    Approximation, not exact calculation.

  • @PhoenixShadow57 start with 100%... now after one year it increases by 70% so now we have 170% of the original... not quite doubled yet (200%)... after another year we are at 289%... past the doubling time now... but to calculate the exact doubling time we take the natural log of 2 multiplied by 100 which is 69.3147 not quite 70... so you go with 70/69.3137 and you get 1.01 roughly so shortly after the first year youll hit the doubling point...

  • @PhoenixShadow57 the problem that you ran into was you tried to take 70 and divide it by 70 but the natural log of 2 isnt quite 70... hope that helped...

  • /watch?v=4GyVFfV2Olk

  • This man 's wall-of- math has to keep getting bigger and bigger for his growing heart to hide behind. I can't watch.

  • This Is The Most IMPORTANT Comment You'll Ever See.

  • Comment removed

  • this video convinces me in how much really hate math! and i have a test in the subject tomorrow.

  • BOOOOOOOOOOOOORRRRRRIIIIIIINNN­NNNNGGGGGGG

  • I think the most important thing you learn is at 7% interest your debt will double in 10 years. If you pay off 7% per year/month it halves the time you would take. i think....

  • This shit is crude and simplistic. This is what happens when you have a math teacher who thinks that by adding along a single qualitative vector you can explain authoritatively social reality. It's this type of bullshit that informs policy in this country and makes us weak, and not only that, leads to policies that brutally exploit the third world because, in our view, they need to be kept in check. A lot of self-serving horseshit right rhetoric right here.

  • @zacbra amen to that!

  • @zacbra I am just wondering by your comment why you even bothered watching and even more why not just close the vid and go watch another one?

  • @philosophicalreason

    i'm just wondering how zacbra could have said that without watching it...

    It's called intellectual honesty, with a tad of logic. Just maybe.

  • that's gamin!

  • I bet that even many of the people who work with exponential functions lack the intuition for what exponential growth really means. Great lecture series! If you want to keep on learning something new every day, visit bits4memes. Not the most important blog you'll ever see, but pretty good!

  • 2013 = 160$? LOL it is like hardly that much NOW and it is 2012

  • haha suckers clicked on this video.

  • @thedarkshitstain There won't be enough. If PO is real you'll end up needing to either be skilled in farming, hunting or foraging. Or cannibalism in the worst case scenario.

  • QUICK go buy canned food.

  • you cant run out of electricity , you make electricity by fuel ,power,heat ,wind .We cant run out of wind or waves.

  • @steviesuperstar

    Agreed. Saying we are going to run out of energy is as fucking retarded as saying we are going to run out of matter. For a bunch of alleged scientists, the commie environmental movement knows fuck all about physics or any other science for that matter.

    P.S. A Watermellon is someone who is green on the outside and red on the inside.

  • While, technically a true statement, the fun part of the fact is we WILL run out of the stuff we use to produce energy with at this point in time. The trick is finding a new resource for producing the energy we need BEFORE we run out the resource we currently use, fossil fuels. Do you think there is a bottomless oil pit? Oh I get it, we just haven't found this UNLIMITED supply of oil yet, what was I thinking? Everything is limited, albeit quantities can be HUGE.

  • @chipstack1980

    "Do you think there is a bottomless oil pit?"

    It seems to me that the logical thing to do regardless of would be to get the government out of the way, end the regulatory capture and allow for competition. The reason we have problems is because it's run by the equivalent of the post office. What you want is UPS and FedEx. We wouldn't even be having this conversation right now if Clinton hadnt ended the telco monopoly in 1996.

  • @sanitydotorg Whilst energy is only borrowed, it is still transferred away from one system and into another, where it may be difficult or almost impossible to retrieve. When eat food, you put that energy into other processes. Exercise releases energy as heat, whilst your muscles use energy for motion, as does your brain for thought or rather electrical energy..... Is it lost? No. Is it transferred elsewhere? Of course. Can you get it back? Highly unlikely. It's no longer useful.

  • i.e. the law of entropy.

  • @sanitydotorg By the way, you come out of your fox hole now Bunny. America stopped fighting Communism a few decades ago.

  • @darcybombdiggy

    Really? Every single plank of the communist manifesto has been implemented in the united states. The more you talk, the more obvious it becomes that you are not only a sociopath, but a deranged psychotic as well.

  • @steviesuperstar Technically you can. Wind contains a finite amount of energy. If you take too much energy out of the earths wind systems, eventually you will affect the planets wind cycles, hence affecting numerous weather fronts, rainfall patterns, storm formation, etc. Wind / Tidal power takes energy out of established weather systems. Building too many of these would result in diminishing returns of energy. Get less out than you put in etc. Therefore we need to understand these limits

  • @steviesuperstar Try this out for size, google

    'new scientist wind and wave farms could affect earths energy balance'

  • @darcybombdiggy yeah thanks , i read it , im not convinced though these guys are always getting things wrong. there is solar energy though that was mentioned at the end of the artical . this i think is the way forward also

  • the end is near !

  • dont watch it! it will make you learn stuff!!

  • BOLLO IS SERIOUS BUSINESS!!!

  • Wow!! this is really The Most IMPORTANT Video You'll Ever See!!

  • Exponential growth is just a mathematical abstraction. Things don't grow at a percent. They grow by a certain length. That's why small economies grow "faster" than large ones. China has fast growth because, compared to their population, they have a small economy. It's not a matter of mathematical causation. Things growth until they can't, then they stop. It's not surprising or terrifying.

  • So this explains why my cock keeps growing

  • I thought it was Chevy Chase :P

  • sanitydotorg is a classic example of a retardness that is going to kill us all.

  • I agree this is a very useful things to know. But what does that have to do with the price of tea in China?,,,in other words, the price of tea actually representing human relationships which is the only way we can make our society better, the only way to stop the horrors of war, famine etc....in other words we are taking about how to love each other....now that is the real price of tea. Thanks for this though!

  • weeeeeeeee ouou weeeeee ouou. That is the 27009th most IMPORTANT series of letters you will ever see.

  • this is in Boulder Co! if anyone has ever been there its pretty much a college town in colorado with the pearl street mall full of college hippies playing bongo drums and openly smoking weed everywhere lol every store even gas station has a couple "tobacco bong" for sale all these students are probably stoned right now haa

  • The biggest threat to the human race is that douche bags like this don't understand basic Economics. You can't run out of resources. As something becomes more scarce, the price goes up, encouraging people to search for alternatives. Thanks for playing today on you're a whack job communist with a paranoid conspiracy theory.

  • @sanitydotorg Oh yeah, you're right. Hey, HANG ON! I thought, if something was scarce it means its almost gone.... isn't that what the 'scarcity' law was trying to avoid? But you can just move on to something else and use that til' its scarce too? Then soon enough everything is EQUALLY scarce and we're nearly out of everything! Sounds like a market failure to me....right?

  • @darcybombdiggy

    No. There is no such thing as market failure. There is only government failure. No amount of your frothing, sociopathic raving will ever provide you with a unicorn or create more coal. Despite 4000, years of government terrorism and democratic trolls destroying the productive class, the state has accomplished nothing but destruction. All the legislation in the history of the world has failed to produce as much as a single loaf of bread.

  • @sanitydotorg Haha. 'There is no such thing as market failure' - haha. Lost all respect for you that instant. I can tell you're a zealot, look closely at yourself and your comments and you will see you're full of fervour. Check yourself before you wreck yourself. Goverment is not perfect, neither is the market. In fact, in the last 150 years, the two are one and the same. Clearly you're not ready to accept that though. Sucker

  • @darcybombdiggy

    How is government the same as the market? The market is based on voluntary, free association to the benefit of all parties involved. The government is based on compelling people to do things the wouldn't do voluntarily with the barrel of a gun.

  • @sanitydotorg Wow. Do you understand what marketing is? Because if you do, you'll understand that large sectors of the business community use it to control and influence what you think, do and BUY. It's based on the principle that appealing to your emotions (in this case a sense of anger and frustration with society) can heavily influence your thoughts, actions and opinions. Government and the Market have a close relationship, e.g. Dick Cheney - Defence Secretary, Vice President..CEO Halliburton

  • @sanitydotorg The market does not exist without a government to enforce contracts and protect property rights. There are no rich hunter gatherers. Keep living in a fantasy land.

  • @TacticusPrime

    The government protects property rights? That sir is pure, raving psychosis. Sounds like you're the one who is living in fantasy land. Government was created to commit crime not prevent it. All effective defense is private.

  • @sanitydotorg You think the mass of the poor would respect the right of the wealthy to merely "own" and not work when they could simply take from them? Remember the French Revolution? Humans exist in community. They have since before they were fully humans. In early human communities no one could become rich because everything was shared (and carried place to place). Governments were created by the wealthy minority in cities to maintain their sedentary wealth.

  • @TacticusPrime

    "You think the mass of the poor would respect the right of the wealthy to merely "own" and not work when they could simply take from them?"

    That's why we have private security and firearms ownership. Besides, most people are cowards. That's why they invented the voting booth so they had something to hide behind when they rob the productive class. It takes courage to put a gun to someones head. It takes none at all to press a button on election day.

  • It doesn't take courage to point a gun at someone, in my opinion, that's cowardice. I think people who use guns are doing so because they are motivated by fear. Think about it. It's super easy to pull a lousy little trigger, if you can stomach the mess it will make. Could you stand in front of a lion, for example, and face him off empty handed? If I gave you a gun and a choice, what would motivate you to kill the lion with the gun? FEAR of being eaten or mauled by the lion-IDIOT

  • @chipstack1980

    "It doesn't take courage to point a gun at someone"

    It takes a lot more courage than voting. At least there's risk involved.

  • @sanitydotorg There's risks and consequences in everything anyone does no matter how small. Cause and Effect.

  • @ShiznitXD

    Right. I was talking about a priori risk. TacticusPrime was claiming that it does not take any more courage to commit an armed robbery than it does to vote in an election.

  • @sanitydotorg It doesn't take any courage at all to use a firearm. Just desperate ruthlessness, which the poor would have in abundance in the libertarian dystopia.

    Just to be clear, you want America to become Somalia and you're arguing that that would be a good thing?

  • @sanitydotorg And when something becomes or is purported to be 'scarce' it's more valuable to anyone who can control it

  • I find it disturbing how few people who has actually seen this through after seing this part.

    Also, everyone who finds this interesting or even frightening should really watch chris martenson's "Crash Course" also found on youtube.

  • chuck norris the most important man ever!

  • Comment removed

  • this is a man who loves his functions!

  • this is the MOST improtant comment you will never see! XD

  • Comment removed

  • What the FUCK? His explanation of "where did the 70 come from" is "it's 100 ln 2, it's all very logical." Thumbs up if you think he has NO IDEA why you would multiply 100 by ln 2.

  • @greg55666 That is exactly what he is talking about, that fools like you don't understand mathematics.

    Here is an attempt to make you understand. Do the following:

    1. Take a number X (take 100 for simplicity), add 5% of X (5, if X=100) to it, result is "X + 5/100*X" (105, if X=100)

    2. Replace X (100) with "X + 5/100*X" (105) in the first step

    Repeat the two steps 14 times, and at the end of 14th iteration you will have X as approximately twice (~198) of what you started with (100)

  • @mishrasetu Man, oh, man. I'm just guessing here--you'll have to tell me if I'm right: you do not even know what "natural log" is, am I right? That is why you would repeat this third-grade math lesson as if you are explaining something profound to me? My question is WHY NATURAL LOG 2? It must have something to do with series (and it's easy to see why it has something to do with logarithms generally), but why log 2? How did he DERIVE that? Have you ever heard that word? DERIVE?

  • Comment removed

  • @mishrasetu Why did you remove your comment? Did you realize I wasn't asking about the formula for compound interest, I was asking where the LOG 2 comes from?

    Also, I have never needed a formula for compound interest. Just type it into excel and then pull down.

    I'll bet you can't tell me how to derive the formula you just gave me! I'll do it for you if you would like.

  • @greg55666 I didn't removed it, probably Google/YouTube auto-bot did. It had a link, you see. I wish I could re-write it all, but I don't have the liberty of time. Moreover, there are word count and formatting restrictions in youtube comments, that make it painful to put a mathematical derivation out there. However, you must have got the comment as an email.

  • @mishrasetu Oh, whoops, I didn't actually look at your post. Sorry about that. I just saw that you actually did make a stab at explaining where the ln comes from. Thank you, you actually answered my question . . . sort of. The real question was, why e at all? Going from e to ln as you do is really just a manipulation--how is the formula derived?

    Seriously, sorry about that, I actually read your post and see you're about 100 times smarter than the average youtube user.

  • @mishrasetu Ooohhh, I just looked at the wikipedia page you sent me. I understand now. The log 2 isn't really necessary, in fact it's inaccurate. e comes from CONTINUOUS compounding, except of course that is not what happens in real life.

    I suppose it's okay to do it that way, it is one of those utterly needless complexifications that economists are so fond of to hide the fact that their profession only needs 3rd grade math.

  • @greg55666: It's not necessary to have continuous compounding at precisely the same rate to derive the same result. 7% one year, 6% the next, then 8% and so on.

  • @greg55666 In real life population growth does happens continuously. Maybe not as continuous as nuclear decay. And not if you take an interval of nano-seconds, but sure do if your interval is in seconds. Which is good enough for all practical purposes.

    But I do understand your point, The rate of growth given is in per year basis and not the continuous rate of growth. But that doesn't affects the principle. Best it can add a year or two to the doubling time. You are still doomed if it continues.

  • @greg55666

    If A = B^x, then x = 'log of A to the base B' OR 'log (base B) A'

    And this a fine piece of mathematics (if B not equal to 1), comes directly from the definition of Logarithm.

    Now any log to the base e is said as 'Natural Logarithm' and represented as 'ln'

    So, if B = e

    (As is in our case, assuming continuous compounding, which is the case if you take PGR, Population growth rate. It is a continuous growth rate NOT yearly). Equation becomes:

    x = ln (A)

    Is that what bothered you?

  • @mishrasetu Oh I see, it's like complex analysis--it's an initial complexification that leads to dramatic simplifications further down the line. It's a weird move to "approximate" what is naturally discrete with a continuous function (the opposite of how we normally think). But the reason to do it is it makes functions regarding rate of change--the derivative of e^rt--super easy. Very interesting.

    For the first time I think EVER for me on youtube, you answered my question! Thanks!