Real World Examples of Periodic Functions

Real World Examples of Periodic Functions

There are two types of stocks; cyclical and non-cyclical. Stocks always depend on the market and the success of companies comes from consumer demand. When people make purchases they make two different kinds of purchases. People will always need to make purchases for necessities such as electricity. However, whenever the economy is doing well, people have the ability to buy things that they want. This is what determines the difference between cyclical and non-cyclical stocks. Non-cyclical stocks are the stocks that no matter what the state of the economy, people must buy them. Cyclical stocks consistently rise and fall. Whenever the economy is doing well, then people will make purchases in these cyclic stocks. Investors usually try to time the market when buying stocks at the low point and selling it at its highest point.

Review the graph of the stock of Direct TV

http://finance.yahoo.com/echarts?s=DTV+Interactive#symbol=dtv;range=1y;compare=;indicator=volume;charttype=area;crosshair=on;ohlcvalues=0;logscale=off;source=;

Practice

-look at the 6 month and/or the 1 year graph of the stock

-notice the high points of the graph and try to estimate the period of the graph(use the volume right under the graph to help you find the high points of the stock)

-using other things you know about periodic functions try and see if you can identify other parts of the graph

-try and come up with an equation using your predicted period

-find other examples of cyclical stocks

Graph of Direct Tv

Real World Problem

Tidal Waves

The water depth in a harbor is 20m at high tide and 10m at low tide. One cycle is completed approximately every 12 hours.

Find an equation for the water depth as a function of the time, "t" hours, after low tide.

answer: y = 5sin30x (t-3pi/2) +15

Here are my biorhythms for the next month or so.

Cyclical Stocks

What are tidal waves?

Tidal waves and tides are the result of the gravitational pull of the moon and sun. Although tides are not consistent around the globe, they always cause a rise and fall in sea level. A tidal wave results in an extreme discrepancy in water level between high tide and low tide, and that change often occurs in a very short period of time. More specifically, tidal waves are common in narrow bays or rivers along the coast. The intensity of a tidal wave varies depending on its location. However, more often than not, tidal ways are not visible, unless one were to watch the change in tide for multiple hours. Although the two are often confused, tidal waves and tsunamis are very different. A tsunami is the result of a shift in the tectonic plates, in the ocean, otherwise known as an underwater earthquake. This causes a massive surge of water onto land. However, tidal waves are not known to be nearly as physically destructive.

Biorhythms

By Alison, Nancy and Clay

Some believe that cycles called biorhythms play a significant role in determining how people function in a few main areas: physical, intellectual and emotional capability. And, you guessed it, biorhythms behave just like trigonometric, periodic functions. While biorhythms are not scientifically proven, to say the least, with or without realizing it, people definitely experience noticeable swings in mood, mental capability and physical performance as time goes on. For these patterns, biorhythms offer some possible explanations that indicate when during the day or the month one will be at his or her best in one of the given domains, depending on that person's birth date. So if you have a first date or a job interview, check out your biorhythmsand plan accordingly.

Here is a more simple example that illustrates how biorhythms work.

The physical pattern lasts 23 days, the intellectual 33 and the emotional 28. Each pattern has a specific equation (where t is equal to the days after the birth date):

So here's your biorhythms problem!

Using the biorhythms equations, graph your own biorhythm for the next month or so. After that, you learn that you're bipolar, which results in your behaviors occurring 2 days earlier then they normally would. Please take that information into account with a new graph. Finally, as a result, your doctor prescribes some medication, but you take too much which results in your biorhythms experiencing increases and decreases, 2x their original amplitude.