Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

 $A\left(n\right)$________ is a function of the form $f\left(x\right)=C{a}^x$ where $a>0, a\ne 1,$and $C\ne 0$ are real numbers. The base $a$ is a ____ and $C$ is a _____.

Step-by-Step Solution

Answer

A(n) exponential function is a function of the form $f\left(x\right)=C{a}^x$ where $a>0, a\ne 1,$ and $C\ne 0$ are real numbers. The base $a$ is a growth factor and $C$ is a initial value.

Step 1. Given

$A\left(n\right)$________ is a function of the form $f\left(x\right)=C{a}^x$  where $a>0, a\ne 1,$ and $C\ne 0$ are real numbers. The base $a$ is a ____ and $C$ is a _____.

Step 2. Exponential function

An exponential function is a function of the form $f\left(x\right)=C{a}^x$ where $a$ is a positive real number $a>0, a\ne 1,$  and $C\ne 0$ is a real number.

The domain of f is the set of all real numbers. The base a is the growth factor,

And because $$\begin{gathered} f\left(0\right)=C{a}^0 \\ =C \end{gathered}$$, we call C the initial value.

Step 3. Fill in the blanks.

$A\left(n\right)$ an exponential is a function of the form $f\left(x\right)=C{a}^x$ where $a>0, a\ne 1,$ and $C\ne 0$ are real numbers. The base $a$ is a growth factor and $C$ is a initial value.