This is the problem that we face, due to the doubling caused by Exponential Growth.

HAPPY ENDlNG

Underpinning much of this is technology, and of late, exponentially growing technologies.

And now I'm going to take the most extreme of all steps.

In other words, the rate of increase is exponential.

Information technologies double their capacity, price performance, bandwidth, every year.

Exponential growth, that's the key here.

So the idea here is just to show you that exponential functions are really, really dramatic.

First they don't grow.

What do you think you have in a month? We're at a billion.

You could buy 10 million in 2002.

And I was asked, Well aren't you nervous?

We'll then go to the next paradigm.

You know, you all have smartphones, we're all connected to the web.

So we know the basic trig functions.

I put 49 famous computers on this logarithmic graph by the way, a straight line on a logarithmic graph is exponential growth that's another exponential.

We'll see the same thing in the economic recession we're having now.

less powerful than the computer in your cell phone.

Centuries after his crucifixion Christ's followers had grown exponentially and had started a religious war against the pagans.

Layered, like nachos. Exponential growth.

Well, I have to raise it to the second power.

And Moore's Law was not the first paradigm to bring exponential growth to computing.

Returns TRUE on success or FALSE on failure.

Uh,in your case,I'm guessing the progressionis exponential.

And its solution isn't a number, its solution is a function, or a set of functions, or a class of functions.

And you can also type help rand.

50 different ways to measure this, the number of bits being moved around, the size of the Internet.

And every time they turn themselves over there is some damage.

So how do we study properties of clusters as a population?

So sort of, if you continue down here, you're gonna see vacuum tubes show up.

Exponential function

We know that the first 10 years of a career has an exponential impact on how much money you're going to earn.

And in a trillionth of a second it expanded exponentially into what became the universe we know.

Here, we're creating a function using lambda.

The histogram filter's biggest disadvantage is it scales exponentially, and the reason is any grid that is defined over arcade dimensions will end up having exponentially many grid cells in the number of dimensions, which is really unfortunate because we can't really represent high dimensional grids really well.

We've already had very good models and simulation of about 15 regions out of the several hundred.

Okay, let's say you're me and you're in math class and you're supposed to be learning about exponential functions, but you're having trouble caring about exponential functions because unfortunately your math class is probably not terribly engaging.

With that we already solved the problem.

It's exponentially improving. Now, exponential is an overworked word.

We've had productivity go from 30 dollars to 150 dollars per hour of labor in the last 50 years.

Let's calculate how much money we have earned.

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But our brains are wired for a linear world.

The particle filter is the easiest to implement, but the complexity scales exponentially with the number of dimensions.

In this video, I want to introduce you to the idea of an exponential function and really just show you how fast these things can grow.