Lesson27 - MA 15200 Lesson 27 Section 4.1 We have discussed...

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1 MA 15200 Lesson 27 Section 4.1 We have discussed powers where the exponents are integers or rational numbers. There also exists powers such as 3 2 . You can approximate powers on your calculator using the power key. On most one-liner scientific calculators, the power key looks like Enter the base into the calculator first, press the power key, enter the exponent, and press enter or equal. Ex 1: Approximate the following powers to 4 decimal places. 32 4.8 ) 2 _________________ ) (2.3) ________________ a b I Exponential Functions A Basic exponential function f with base b is defined by ( ) or xx f x b y b  , where b is a positive constant other than 1 and x is any real number. A calculator may be needed to evaluate some function values of exponential functions. (See example 1 above.) Many real life situations model exponential functions. One example given in your textbook models the average amount spent (to the nearest dollar) at a shopping mall after x hours and is ( ) 42.2(1.56) x fx . The base of this function is 1.56. Notice there is also a ‘constant’ (42.2) multiplied by the power. Be sure to follow the order of operations; find the exponent power first, then multiply that answer by the 42.2. Suppose you wanted to find the amount spent in a mall after browsing for 3 hours. Let x = 3. 3 (3) 42.2(1.56) 42.2(3.796416) 160.2087552 f To the nearest dollar, a person on average would spend $160. x y The following are not exponential functions. Why? 3 ( ) ( ) 1 ( ) ( 4) ( ) x f x x f x f x f x x  
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2 II Graphing Exponential Functions Ex 2: Graph each exponential function. x y a 2 3 ) x x f b 3 1 ) ( ) There are several exponential graphs shown in figure 4.4 on page 415 of the text. After examining several graphs, the following characteristics can be found.
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Lesson27 - MA 15200 Lesson 27 Section 4.1 We have discussed...

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