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# Graphs of Exponential Functions

## Growth and decay functions with varying compounding intervals

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Why Do People Invest in the Stock Market?

Why is investing important? Why are people so fascinated by the stock market?

#### Why It Matters

Everybody works to earn money and to save a little for later in life. The appeal of investing lies in the concept of compound growth, which relies on exponential functions.

Investors buy a part of a business, or a share, expecting the business to grow and the share to increase in value. If you bought the share for $100, you might expect its value to go up by 10%, which means that at the end of the year it would be worth$110. You have earned $10. In the second year, how much did you earn? Another$10? No, because you earned 10% not on $100, but on$110. You earned on the earnings of the previous year. This is referred to as compounding.

If you kept the share for 30 years and it hadn’t compounded, it would be worth $400 by then. However, if it had compounded every year at 10%, it would be worth about$1,750! People invest in the stock market hoping to make lots of money.

Unfortunately, in real life, not every company grows, and not every company grows every year, making the stock market much more complicated.

See the power of compounding for yourself: http://www.youtube.com/watch?v=XUCYdGAWcbo

#### Explore More

Here is another example of exponential growth. A chessboard is made up of 64 squares. Suppose you put one grain of rice on the first square, two on the second, four on the third, eight on the fourth, and so on. How many grains of rice would you end up putting on the 64th square? The answer is 19 million trillion—that is, 19,000,000,000,000,000,000 (19 followed by 18 zeros)!

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