Question

-8Intro-4-2864yf(x) = 3 (2)48XConsider the exponential function: f(x) = 3[*The initial value for this function is VThe base for this function is

Answer 1

Explanation:

The function is given below as

$f(x)=3(\frac{5}{4})^x$

Concept:

An exponential function is a function in which the variable is an exponent. Exponential functions are written in the form f(x)=ab^x f ( x ) = a. b^ x . Initial Value: The initial value of an exponential function is the result of substituting x=0 into the function.

Hence,

by putting x=0, we will have the initial value be

$\begin{gathered} f(x)=3(\frac{5}{4})^{x} \\ f(0)=3(\frac{5}{4})^0 \\ f(0)=3 \end{gathered}$

Hence,

The initial value is

$3$

Part B:

The genral equation of an exponential equation is given below as

$\begin{gathered} y=ab^x \\ a=constant \\ b=base \end{gathered}$

By comparing coefficnets,

The base for this function is

$\frac{5}{4}$

Part C:

The domain of the function is given below as

$\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:Part D:

The range of the function is given below as

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$