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Unformatted text preview: Math Learning Center Boise State ©2010 Exponential functions: week 13 Business As we have seen, exponential functions describe events that grow (or decline) at a constant percent rate, such as placing capitol in a savings account. Exponential functions will have a role to play in Borrowing and lending; investing; discounting; and growth of companies. Many of these equations need additional mathematics topics such as series and sequences learned later in mathematics. As this is the first experience for many into exponential functions we will spend today focusing on developing a deeper understanding of exponential functions, increasing the learning opportunities when exponential functions reappear. The simplest form of an exponential function is gG¡¢ £ ¤ ¥ where u ¦ ¤ ¦ U or ¤ § U . Note: the letter ¤ is used in an exponential function as it represents the “base of the exponential function. Let’s start with ¤ § U , let ¤ £ ¨©ª «¬ ®¯ Graph the three functions: Describe the characteristics that all three graphs have in common. Did you catch the relationship of the value of g G¡¢ °±²¬ ¡ £ u³ One relationship that is generally not seen by most students when they begin to study exponential functions is that as ¡ ´ µ¶ the answer, gG¡¢ gets closer and closer to the xaxis but never reaches it. gG¡¢ £ ¨ ¥ ¡ gG¡¢2 1 0 1 2 gG¡¢ £ ª ¥ ¡ gG¡¢2 1 0 1 2 gG¡¢ £ ® ¥ ¡ gG¡¢2 1 0 1 2 The notation ¡ ´ µ¶ is read “as x goes to negative infinity.” The arrow means “goes to”. The sentence “as x goes to negative infinity” implies that we are considering what happens to the graph as x moves further and further to the left on the xaxis. Math Learning Center Boise State ©2010 This type of behavior is called asymptotic behavior. And it is said that these three functions are asymptotic to the line g G u ¡¢ £ ¤ ¥U . So we have an idea as to what happens if ¦ § ¨ . Let’s know consider when u © ¦ © ¨ . Graph the following functions....
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 Fall '09
 ALINASCHIMPF
 Math, Algebra, Exponential Function, Derivative, Exponential Functions, Math Learning Center

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