Question

What is exponential function definition?

Answer 1

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:

$$\begin{gathered} f\left(x\right)=b^x \\ f\left(x\right)=a{b}^x \\ f\left(x\right)=a{b}^{cx} \\ f\left(x\right)=e^x \\ f\left(x\right)=e^{kx} \\ f\left(x\right)=p{e}^{kx} \end{gathered}$$

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 $f\left(x\right)=a^x$.