To determine the initial value when Chelsea is graphing the function [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex], we need to find the value of the function when [tex]\( x = 0 \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 20 \left( \frac{1}{4} \right)^0
\][/tex]
2. Simplify the exponent:
[tex]\[
\left( \frac{1}{4} \right)^0 = 1
\][/tex]
Any number raised to the power of 0 is 1.
3. Compute the function value:
[tex]\[
f(0) = 20 \times 1 = 20
\][/tex]
Thus, the initial value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex] is 20. This means Chelsea's first step in graphing [tex]\( f(x) \)[/tex] is to plot the point [tex]\((0, 20)\)[/tex] on the coordinate plane.
So, the graph representing her first step will show a point at coordinates [tex]\( (0, 20) \)[/tex].
