# 4.1.notes - < e< 3 we have that for x> 0 2 x< e...

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MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing- han Meng On exponential functions Example . The graphs of four functions are shown in the following diagram. They are f ( x ) = 2 x , g ( x ) = e x , h ( x ) = 3 x , s ( x ) = e - x . Match the functions with graphs: x K 2 K 1 0 1 2 1 2 3 4 5 6 7 8 9 Solution. Note that only the blue graph represents a function with exponential decay. Thus, the graph of y = e - x is in blue. The pink, red and green graphs represent functions with exponential growth. In order to distinguish them, we note that since 2
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Unformatted text preview: < e < 3, we have that for x > 0, 2 x < e x < 3 x . Thus, the graphs of y = 2 x , y = e x , y = 3 x are in green, red and pink respectively. Please note that (a) Exponential functions are of the form y = b x , where the base b is a positive constant. (b) The graphs of y = e x and y = e-x are mirror images of each other about the y-axis. (See the graphs in red and blue above.) The same is true for y = b x and y = b-x for any b > 0. (c) The function e x is sometimes written as exp( x )....
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