### Examples

1.

If the price is here, then it makes sense to produce up to that amount of oil.

2.

Any more and a barrel of oil would cost more to produce than what it sells for.

3.

If the oil price moves up, though, then it makes sense to increase production

4.

even when it raises the cost per barrel,

5.

and that’s what happened for most of the last 50 years.

1.

So if you use FM, it's going to be the frequency timing, right?

2.

- Right.
- If you're using AM, it's the amplitude.

3.

- Right.
- I can apply that all over the RF frequency space.

4.

I can go to a very low megahertz range,

5.

and I can send out AM,

6.

and I can get that atmospheric propagation, that bounce.

7.

- Okay.
- But if I move up to the higher frequencies,

8.

- it'll punch right through the atmosphere.
- Got it, got it, got it!

1.

Now, let’s switch to some sine waves.

2.

This is again 1 kilohertz.

3.

This looks perfectly smooth, no stair-steps to be seen.

4.

To be fair, though, even in Audacity, it looks pretty good.

5.

Let’s move up to a 10 kilohertz sine wave.

6.

Now, in Audacity, it looks really gnarly, with the connections between the samples making a barely intelligible wave.

7.

There aren’t even 5 samples per cycle, so how can the smooth detail of the sine wave possibly be reproduced?

8.

Well, take a look. There’s a perfectly smooth sine wave for you right there.

1.

We want each interval to be 1 floor smaller than the last.

2.

This equation can help us solve for the first floor we need to start with in the 100-floor building.

3.

There are several ways to solve this equation, including trial and error.

4.

If we plug in 2 for n, that equation would look like this.

5.

If we plug in 3, we get this.

6.

So we can find the first n to pass 100 by adding more terms until we get to our answer, which is 14.

7.

And so our thief starts on the 14th floor,

8.

moving up to the 27th, the 39th, and so on, for a maximum of 14 drops.