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hey guys this is Khalid here I just want
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to give you a quick overview about the
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key insights about e this is essentially
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what I wish it could have gone back in
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time and told myself about e you know
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way back in high school already here we
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go okay e is essentially epitome of
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universal growth what does that mean why
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is it universal well we can start off
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with regular growth if you consider
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something that changes over time like a
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simple progression is doubling right so
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you are a time one you have certain
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amount of time to you double a time
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three you double again so you have four
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and so on and you basically have some
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kind of exponential curve and then we
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can call this two to the X so that's so
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amount of time you know as you go along
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you basically get some amount of growth
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happening now this might seem Universal
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and it is for a few reasons the first is
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that - that's 100% growth which
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basically means that you're doubling by
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the amount that you have so it's kind of
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universal that sense right it's a unit
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growth so if you want if you triple
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that's kind of you know 200 percent
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growth which is you know it's not
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exactly is clean as 100 percent growth
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so there is a cool kind of you know
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symmetry here where you're growing by
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the amount that you have so basically
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this goes here and then you get a new
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interest and then these go here and you
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get new interest as well so 100 percent
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is kind of a neat idea but there's a
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problem you waited until the end of the
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period to get all your interest
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you had nothing you were just normal
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then suddenly boom this guy popped in
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out of nowhere and this actually isn't
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that common right if you think about
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natural processes things don't just
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appear out of nowhere they grow slowly
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over time for example take a look at a
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cell if we start with same idea of
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growth we might have a cell and over
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time it has a little buddy and this
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little buddy
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is kind of emerging out of them right
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and eventually it'll pop out so it
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didn't pop out all of a sudden over time
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it's sort of emerged and then each day
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got a little bit more and finally it was
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a new soul of its own so the idea is
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that instead of getting all your growth
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at the end which happens with
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to to the X that we saw kind of like a
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staircase right it sort of goes up like
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that we're talking about kind of as more
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smooth gradual growth so if you think
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about this this is actually the more
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like nature right in nature things grow
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slowly over time they don't sort of
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suddenly appear out of nowhere and have
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a kind of a discontinuous jump so if you
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really want to have a universal way to
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talk about growth it really should be
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more of a smooth change instead of kind
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of a staircase like pattern because
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really that never happens things you
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know don't happen isn't aeneas lee it
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happens over time now there is one
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little side effect though when we're
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growing this cell it couldn't actually
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grow on its own we sort of waited until
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we had a red cell and then that red cell
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could start having its own interest like
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a green cell coming out so we have a red
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cell and then we have a green cell
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emergent right so the red was kind of
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stuck in the green started coming out as
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well so this again isn't quite as smooth
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as it could be because while we're
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growing the red the red can't grow on
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its own and one kind of neat thing is
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that money actually it's a good example
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of something which doesn't have this
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problem so here's the idea if you're
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looking at the way money grows we might
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have one dollar and over time it's a
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dollar but you know what it earns
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interest so as time goes on your dollar
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earns interest and eventually you have
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the new dollar shiny new dollar all for
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yourself but the cool thing is that with
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money interest can earn interest so this
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red amount that you earned well that can
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own own its own interest here which kind
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of shows up here and this green interest
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well it can earn its own may Brown
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interest that shows up here as well if
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you look at the article there's kind of
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a worked example but the idea is this
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your regular amount come goes along like
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that it earns some interest which is
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this kind of red growth here and that
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red growth well that earns its own
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interest which is this kind of green
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growth here and that green growth earns
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its own interest which is this brown
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growth and so on so there's actually an
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infinite amount of growth happening and
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it sort of looks like that so what ends
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up happening is you get this curve which
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has sort of an infinite number of
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opponents the biggest components come
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from these kind of giant chunks in the
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beginning but you end up having smaller
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and smaller groups emerging so it's a
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bunch of little slices and eventually it
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caps out here's the idea
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E is that cap so if you add up all the
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slices you get growth which is actually
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e to the X so E is basically the idea of
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taking growth adding its and Trust
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adding bats interest adding bats
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interest and so on and so on and each
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time you do it it gets a little bit
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narrower and narrower and the max speed
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limits you hit that's e so the reason is
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Universal is the following one it's 100%
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growth so the idea is that your original
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item it'll actually double itself at the
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end of one period so you start at you
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know let's call this time zero at the
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end of one period your black amount has
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actually doubled itself so that's why
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it's how 2 percent growth but two it's
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continuous and this is really the key
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here it's not jumping suddenly as time
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goes on each instant is earning red and
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the eds
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the Reds earning green and the Greens
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earning brown and the Browns earning
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gray and so on and so on so this
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combination actually that gives you some
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amount of growth at the end of the
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period which is about 2.718 dot and that
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number is and basically if you want to
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find out how much growth you have at the
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end of two periods or three periods you
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just take e to some exponent so the
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reason that he appears in every kind of
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formula is because it's a very common
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base to verse Allah to talk about growth
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and you can actually change the rate so
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this is actually okay now jumping into
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the kind of flexibility B so E is
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basically 100% continuous growth but
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it's also flexible so E I actually
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consider it e to the RT so this is e to
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the rate times time
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often times the rate is 100% so you
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don't see it because 100 percent is 1.0
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right so you don't actually see it it's
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you know invisible but the idea is that
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if you adjust the amount of interest
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that you get at the end of a period so
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right
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100% let's say you only get 50% interest
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so you'd have something like this you're
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growing and at the end of one period
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you only get 50% not 100% interest you
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still have the same thing that interest
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you know earn some of it yourselves own
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50% and you get 50% of that let's see we
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had brown coming up ended 2% of that
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grey coming up so you still get a
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pattern but it's a little bit reduced
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and the idea is oh in this case it would
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actually be e to the point 5 because
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it's 50% interest and then times the
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amount of time that you want to you take
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it for so you could have 50% interest
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for 2 years and it actually would be the
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same thing as 100 percent interest for 1
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year because 50% times 2 equals 100
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percent times 1 so the cool thing about
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these is really flexible you can adjust
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the rate in time and that works because
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it's based on very universal principles
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100 percent growth and it's continuous
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so there's no kind of jagged edges so
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that's sort of the key insight about e
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the article has some kind of
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computations but here's one little cool
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fact you can actually model the
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staircase like growth so if we have this
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kind of jumpy growth right that's sort
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of appearing out of nowhere e can
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actually match that to some smooth curve
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so that will be e to some interest rate
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I don't know let's call it Q or
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something right so e to the Q that can
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actually match up with any kind of
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jagged interest rate that you want into
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the hood it'll hit all the points so the
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neat thing is that any kind of growth
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can be considered on its own is this
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jagged growth or it can be considered as
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e raised to some interest rate and the
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idea here is that you can actually use
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the natural logarithm to figure out what
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interest rate that is but we'll get to
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that separately so again the ideas
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behind e 100% growth is growing by
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itself you start with something it grows
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and it earns interest it is itself which
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earn some interest on its own and so on
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and so on and also it's continuous it's
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smooth it's not jagged like this it's a
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smooth curve and because of that you can
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vary this growth from 100 percent to 50
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percent growth which actually changes
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the curve to be
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lower and depending on how much you
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angle it you can actually model any type
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of growth that you want so that's my aha
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moment about it's not this magic number
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it's not a magic spell it's just taking
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the idea of growth and simplifying it to
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have this few assumptions as you can be
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growing by yourself a hundred percent
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and don't be jagged and with that you
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get happy mess
