Option A: The first step is plotting the point [tex](0,20)[/tex]
Explanation:
Chelsea is graphing the function [tex]f(x)=20\left(\frac{1}{4}\right)^{x}[/tex]
She begins plotting the initial value.
From the graph, we need to determine the graph that represents her first step. To determine the first step, we need to determine the initial value.
Let us compare the given function [tex]f(x)=20\left(\frac{1}{4}\right)^{x}[/tex] with the exponential equation of the curve [tex]y=a(b)^{x}[/tex]
where
a is the initial value,
b is the change factor,
x is the independent variable and
y is the dependent variable.
The initial value of the function is the value of y which can be determined by substituting [tex]x=0[/tex]
Hence, substituting [tex]x=0[/tex] in [tex]f(x)=20\left(\frac{1}{4}\right)^{x}[/tex] , we get,
[tex]f(x)=20(\frac{1}{4} )^0[/tex]
[tex]f(x)=20[/tex]
Thus, the initial value of the function is [tex](0,20)[/tex]
Hence, the graph represents Chelsea's first step is plotting the point [tex](0,20)[/tex]
Therefore, Option A is the correct answer.
The attached graph shows the result of the correct answer.
