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 _____.

Short answer

A(n)exponential functionis 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-by-step solution

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.