Exponential function

We know the exponential function.

Let's start with an exponential function.

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

So let's just write an example exponential function here.

That's all happening down here. Here's my Gaussian function with the exponential.

So, I kind of took the inverse of the logarithmic function. I wrote it as an exponential function.

Exponential

One way to think about i is that it is an exponential function.

What matters is we have an exponential of a quadratic function over here.

Er, Sir? What's written on the blackboard isn't an exponential function but a trigonometric one ...

It's always good to use the exponential function, because that's easy to take the antiderivative of.

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

So the total running time is exponential. It's not worse than exponential. It's not great.

Write your answer using exponential notation.

The exact formula is an exponential of a quadratic function where we take the exponent of this complicated expression over here.

Prime factorization, and they say exponential notation.

We'll worry about the exponential notation later.

Information technology grows in an exponential manner.

Secondly, the new machine age is exponential.

If you had something growing 5 per year, you'd write the exponential function to show how large that growing quantity was, year after year.

to understand the solution, it's useful to draw the exponential function. e⁰ is 1 and then it goes up exponentially to really large numbers.

log plot is an exponential increase in performance.

But this has progressed at an exponential pace.

We have the tools with this exponential technology.

And that's exponential growth through five different paradigms.

In other words, the rate of increase is exponential.

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

I'm going to write it as exp for exponential .

And that's a very profound explosion of exponential growth.

The universe then underwent an exponential expansion called inflation.

As a result, exponential trends take us by surprise.

However, it turns out that all the arguments of the exponential are at best 0 and otherwise are negative, because the exponential is monotonic that is the larger its argument, the larger its exponential value.

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.

We have exponential computing power and clouds full of data.

One over one plus exponential of minus F of X.

There is a big difference between linear and exponential growth.

Maybe it kind of didn't stay on this exponential progression.

Then the exponential that squeezes it back into the curves.

It's pretty remarkable how smooth an exponential process that is.

So the set of exponential time solvable problems includes NP.

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.

So let's see now how exponential technologies are taking health care.

The Great Depression made not a dent in this exponential progression.

And you can see here that there's an exponential Great Divergence.