Here's what that looks like. This example is more about the evaluation process for exponential functions than the graphing process. We need to be very careful with the evaluation of exponential functions. Definition Of Exponential Function. One person takes his interest money and puts it in a box. Some examples of exponential functions are: Notice that the base of the exponential function, a > 0 , may be greater than or less than one. Even though the base can be any number bigger than zero, for example, 10 or 1/2, often it is a special number called e.The number e cannot be written exactly, but it is almost equal to 2.71828.. The function given below is an example of exponential decay. An Exponential Function is a function of the form y = ab x, where both a and b are greater than 0 and b is not equal to 1.. More About Exponential Function. A function is evaluated by solving at a specific value. Example 3 Sketch the graph of \(g\left( x \right) = 5{{\bf{e}}^{1 - x}} - 4\). This distinction will be important when inspecting the graphs of the exponential functions. The image above shows an exponential function N(t) with respect to time, t. The initial value is 5 and the rate of increase is e t. Exponential Model Building on a Graphing Calculator The formula for an exponential function is y = ab x , where a and b are constants. The number e is important to every exponential function. Here's what that looks like. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828.Thus, the above expression becomes: For example, a bank pays interest of 0.01 percent every day. An exponential function can easily describe decay or growth. Exponential function definition is - a mathematical function in which an independent variable appears in one of the exponents —called also exponential. The general form of an exponential function is y = ab x.Therefore, when y = 0.5 x, a = 1 and b = 0.5. The following table shows some points that you could have used to graph this exponential decay. In fact, it is the graph of the exponential function y = 0.5 x. Exponential functions are solutions to the simplest types of dynamic systems, let’s take for example, an exponential function arises in various simple models of bacteria growth. g(x) = … The term ‘exponent’ implies the ‘power’ of a number. Thus, \(g(x)=x^3\) does not represent an exponential function because the base is an independent variable. In fact, \(g(x)=x^3\) is a power function. The figure above is an example of exponential decay. By definition, an exponential function has a constant as a base and an independent variable as an exponent. An exponential function is defined as a function with a positive constant other than 1 raised to a variable exponent. Exponential Functions. For example, y = 2 x would be an exponential function. For eg – the exponent of 2 in the number 2 3 is equal to 3. 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