Exponential growth, that's the key here.

Layered, like nachos. Exponential growth.

First they don't grow.

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

They do not scale quadratically, in fact, normally they scale exponetially with the dimensionality of the state space because you need exponentially many particles to fill up the state space.

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

HAPPY ENDlNG

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

So we know the basic trig functions.

This is at an early stage, but you can show with the exponential growth of the amount of information about the brain and the exponential improvement in the resolution of brain scanning, we will succeed in reverse engineering the human brain by the 2020s.

Our population and our use of the finite resources of planet Earth are growing exponentially, along with our technical ability to change the environment for good or ill.

We're almost there.

In other words, the rate of increase is exponential.

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

You add the exponents.

To illustrate this idea with a picture imagine we have some function f(n).

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

We'll come back to these.

That's been recognized because the number of particles you need to fill a high dimensional space tends to grow exponentially with the dimensionality of the space.

This is the class I've been using, kind of a parent class for all of my handlers.

But that's just but some number.

In fact, those of you who are still conscious and mathematically competent, will note that this is a semi log plot.

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

Plus 80 .

So they engineered these cells so that when they're growing in the exponential phase, they would smell like wintergreen.

Well, you say, what's the exponential function?

Well, if you increase by 50, you get to 200, so we increased another 25.

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

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

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

And we're all concerned about energy and the environment.

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

Let's go ahead and add our post function to deal with the user types list.

Once we start getting into the positive numbers, we just explode.

Write, render, stern, render those are old.

Exponential function

So for example, let's say that I start with 2, and I say

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

Let's actually use our new verification functions.

If I have the same base 10 right over here, so I can add the exponents.

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

The number of tourists has increased greatly in recent years.

So, if you look at this, this plot, you'll see that, well this roughly looks like a straight line, and a straight line on a

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

Let's calculate how much money we have earned.