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# What is exponential function definition?

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## Definition of Exponential function:Any function of the type $\mathbf{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}{\mathbf{a}}^{\mathbf{x}}$, where $"x"$is a variable and $“a”$ is a non-zero positive constant number and is the base of the function, is called an exponential function. The most popular function is $f\left(x\right)={e}^{x}$ where $e=2.718..$The graph of an exponential function $f\left(x\right)={e}^{x}$ is:Types of the exponential function:$f\left(x\right)={b}^{x}\phantom{\rule{0ex}{0ex}}f\left(x\right)=a{b}^{x}\phantom{\rule{0ex}{0ex}}f\left(x\right)=a{b}^{cx}\phantom{\rule{0ex}{0ex}}f\left(x\right)={e}^{x}\phantom{\rule{0ex}{0ex}}f\left(x\right)={e}^{kx}\phantom{\rule{0ex}{0ex}}f\left(x\right)=p{e}^{kx}$Thus, the exponential function is of the type where $"x"$is a variable and $“a”$ is a nonzero positive constant number and is the base of the function $f\left(x\right)={a}^{x}$.

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