<span>In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = <span>bx</span>, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.</span>
<span>An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.</span>
<span>Before you start, f(0) = 2<span>0 </span>= 1</span>
<span>After 1 hour f(1) = 21 = 2</span>
<span>In 2 hours f(2) = 22 = 4</span>
<span>In 3 hours f(3) = 23 = 8</span>
and so on.
<span>With the definition f(x) = <span>bx</span> and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.</span>
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