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

HAPPY ENDlNG

Exponential growth, that's the key here.

You could buy 10 million in 2002.

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

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

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

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

First they don't grow.

We'll then go to the next paradigm.

Layered, like nachos. Exponential growth.

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

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

Exponential function

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

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

Let's calculate how much money we have earned.

So we know the basic trig functions.

In other words, the rate of increase is exponential.

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

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

But our brains are wired for a linear world.

So, you see, it works just as easily with negative numbers.

Here, we're creating a function using lambda.

Think about the theory of evolution.

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

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.

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

So what do we want to make our v prime?

less powerful than the computer in your cell phone.

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You don't have to have exponents, it's just that these exponents are probably where the motivation for calling these even functions and odd functions came from.

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

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

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

Parentheses..first.

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.

Let's plot that. What I'm gonna do on the right is plot my cost function j.

They don't really know what exponential means, but this is exponential.

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

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

Let's start with a quiz

If we have f(x) x 2, we saw in the previous video that this is even.

With that we already solved the problem.