
Graphs of Exponential Functions Math Help Game Tips:  The relations y=2^{x}, y=3^{x}, and y=4^{x} are examples of exponential functions.  A 'positive constant base raised to a variable exponent' = (constant)^{(variable)} is an 'Exponential function'.  In general, an 'Exponential function' is represented by the formula y=a^{x} where a>0. [Also a cannot be 1.] Notice that for integer a>0, the graph of y=a^{x} passes through the point (0,1).  The relations y=3(2^{x}), y=4(6^{x}), and y=2(3^{x}) are examples of exponential functions with a front multiplier.  In general, a 'Constant times an Exponential function' can be represented by a formula such as y=k(a^{x}). For integer a>0, the graph of y=k(a^{x}) passes through the point (0,k).  In this game, 'k' is an integer from 3 to 3 and 'a' is an integer from 2 to 5.  Notice y=2^{x} has graph points such as (1,1/2), (0,1), (1,2), and (2,4)... , while a relation such as y=2(3^{x}) has graph points such as (1,2/3), (0,2), (1,6), and (2,18)... .  There are many applications of exponential functions. For example, exponentials are used in formulas for compound interest, for geometric growth patterns [a^{x}], and for radioactive decay patterns [a^{x}].  The game can be played using the mouse by itself or using the keyboard by itself.  If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus.  Adjust the game's speed by pressing the + or  key repeatedly. 
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