So this is 8t squared plus I'm just dividing both sides of this equation by 2.

The probability of reaching S prime given that we started state S and apply action A.

We could have also done it other way.

5 minus this 2.

Discount rate

Now what can we do ?

And it just depended on how the mathematics work out.

Another way to kind of just talk about this is to get the present value of 110 a year from now, we discount the value by a discount rate.

Are there special evening rates?

60 off.

Well, I don't give group rates, you know.

We have agreed on the rate of discount.

What is 6 subtracted from 10?

How many is nine minus six?

To compound the amount of money we invest we multiply the amount we invest times 1 plus the yield.

What do I have?

We have agreed on the rate of discount.

Do you have a student fare?

These are 30 percent off.

Perhaps only at a discount.

Are there any discount tickets for me?

We could have said Let y equal the discount

One more thing. With each timetable I draw up... thousands of people's lives are at stake.

So it's v2 dot v1 over the spanning vector dotted with itself, v1 dot v1.

when the sale has a certain percentage ?

And we can do the exercise that we saw on the previous video.

Let's see.

Nairobi, global conference, environmental.

What is it about Superman?

This one's called the median, the lower, and the upper quartile, and these guys are the ones being picked.

And this one that was in Kenya, they went around and distributed to people vouchers, discount vouchers.

Well the antiderivative of y squared and you have to divide by 3, so it's y cubed over 6.

And this was an easy one the answer is 0.

Free coupons. Discount Discount coupons.

And this is scenario three.

But the big learning from this is how dependent the present value of future payments are on your discount rate assumption.

So when someone says, you know, I can use Excel to do a discounted cash flow, that's all they're doing.

So here, for multiple arguments, we have an expression, a comma, and then any more arguments we like.

If I could get it for 90, that's a good deal for me.

So x minus twenty five percent x is equal to the sale price.

On the other hand, we don't seem to have been visited by aliens.

You'd better take his words with a grain of salt.

I get a discount and there's a whole section of books in my area.

But what if I wanted to generalize a little bit ?

Special rates for state and federal employees.