Exponential Function Representation with Natural Base

A horizontal dilation of the graph of an exponential function is equivalent to a change of the base of the function because $f(x)= b^{kx}$ can be expressed as $f(x) = (b^{k})^{x}$ where $b^{k}$ is constant.

To construct a representation of an exponential function using the Natural Base, e, one can express it in an equivalent form using properties of exponents, function composition, and properties of logarithms.

The perspective of an exponential model can be expressed in any base, including the natural base, by leveraging properties of exponents and function composition to represent the model equivalently.

<p>The expression $f(x) = b^{kx}$ is equivalent to $f(x) = (b^{k})^{x}$ because $b^{k}$ is a constant that remains unchanged under different forms of the exponential function.</p> Signup and view all the answers

<p>Using the Natural Base, e, to express exponential functions unveils key graph properties and facilitates a deeper understanding of exponential growth and decay phenomena.</p> Signup and view all the answers