What is the number "e" and where does it come from?

Okay, you have a fact that yes, okay? Good. You'll need it in a second when you hear the word exponential. There are a few different options for this, but

what

is the next word you expect to appear in the phrase growth? I think that's the right exponential growth, and that just means something is growing very fast, right? Well, there is a specific type of exponential growth that exists and

come

s from this. Okay, now exponential growth

does

n't just mean growth that is very, very fast. Well, it means a particular type of growth. Let me put it this way, x squared grows fast, but X cubed grows faster and you know that x to the power of 300 grows faster, okay?

They all grow very fast, but they all have the same type of growth. We call them polynomial growth, none of them no matter how ridiculous this

number

is? None of them are as fast as exponential growth because they do something different, okay? The idea behind exponential growth is that the population is correct, the larger the population, the faster it can grow at this time. They make sense like rabbits. You know that the more rights there are, the faster they can reproduce. It's not just that they will continue to grow faster. It is by their very nature that the more rabbits there are, the faster they can form new families, and that is exactly the same thing that happens with money, the more money you have, the more interest you can earn.

It means more, you're right, in other words,

what

sets electronic cigarettes apart, even if they are so fast, is that it will get faster and faster and it is proportional to the size of something, so the bigger it gets, the You'll go crazy, okay, now think about this. with me. Just think of a particular case. I only have one dollar, right? I don't know if you guys, this if you have five dollars, and you have some interest rates at the other time. That five dollars will earn exactly the same amount of interest as one dollar. dollar here dollar he dollar here Here, do you understand?

They fired them, they backed out for their dollar and just by putting them in a pile of five dollars, they magically don't earn any more interest, you go ahead and hand them the

number

s, that's exactly it. Okay, so I'm going to consider the case of one dollar for every dollar in my bank account. They are all the same. They will all behave exactly the same way. You have to do the same. Okay, now let's assume a very, very generous bank account that gives you one hundred percent interest, okay? Now this sounds generous,

does

n't it? But why do you think in terms of the real world?

A correct population isn't that unusual, if you have rabbits they can literally double and in fact it doesn't take them a year to do so so this isn't that unusual right? So let's consider a year with one hundred percent interest. So this is number one, okay? What will happen to my dollar, what will it be

come

? You will become two dollars and the reason is because if we put one plus the rate is one hundred percent. Which is just ^1, so you get two. Well, now as you know. At least if you're managing money right, they don't wait until the end of the year to pay your extra dollar, okay?

In reality, they are constantly calculating interest and the more they calculate it, you get your money, right? So let's do a little experiment number two, let's say, instead of waiting a whole year. They say they do it twice a year. The semester level is fine now. This is what I'm going to have to do. I'm still getting one hundred percent annual interest, so the father's not going to be as good. How should I adjust this formula? There are two compounding periods, but here's something: what are you going to divide? for 2 instead of getting one hundred percent in the end I'm going to get 50 percent and then I'm going to get another 50 seven so I'm going to get yeah that makes sense so is it equal to?

That's, yeah, one, uh, it's going to be 2.25, nine and four to a quarter, so this is better. This is good right? Well, why do it once a semester and not every month? What formula should I write? Calculators 1 plus 1 12 to the power of 12. Tell me what you get two dollars sixty-three sixty-six one 61 Okay, now this is interesting. Look when I doubled and got an extra 25 cents. It's not bad sex with plus suitable for here. I have become more frequent but I still earn more, but actually thank you. Good. Even more than this right. They will do it every day for you, right?

It's number four, yes, they won't pay it every day, but they will calculate every day. I tend to pay monthly, so what equation should I write? One plus one in 365 and every day they will calculate the interest that she has very little time to point out now. Give me more decimals. Okay, now it's okay. What's going on, right? I would say that from monthly to daily you have increased your cap rate dramatically, but all you have earned is like a few insignificant pennies. Very good, just because. Maybe you think there is something wrong with their computers, forget it every day.

Now we prefer fast computers. Let's do it every minute, okay, another fine. So let's go one plus one each day, 365. How many hours, 24, how many minutes, 60, whatever, okay? 365 24 60 Someone's calculator guess what spoilers it is 2.71828 blah blah blah blah What happened? Now here's the thing, right? I couldn't even get a full game right. I guess you can round up What happened? Well, do you know that all of these are just arbitrary? Well, what mathematicians do is say forget all this for days, months, hours, you and your weak units of measurement. They just say, well, what happens if you say infinity?

Right now in mathematics. We call this a limit because of course you can't do this with infinities, not with numbers. It's just an idea. Okay, but you can take some numbers. You're pretty close. You can take like a million or something like that. Any big number you like, I do it very angry. You made a billion, and I'll tell you right now. You will receive e dollars. Well? This number Just like the cake, I didn't say oh, it better be a certain number. You better get it right, it comes from a structure that exists in nature, i.e. how things grow when they grow relative to their own size or, if you like, how things break down when they disintegrate relative to their own size. own size half-lives that kind of thing radioactive decay Dropping temperatures The hotter something is, the faster it loses temperature, okay?

This is the proportionality number or proportional growth or proportional decrease and that is why it is so important, because that is why it appears on your calculator because it is a number that exists in reality. Just like Pi