To find the initial value of the function [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex], we need to evaluate the function at [tex]\( x = 0 \)[/tex]. Let’s see the detailed steps for this:
1. Identify the function and its form:
The function given is [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex].
2. Determine the initial value:
The initial value of a function typically refers to the value when [tex]\( x = 0 \)[/tex].
3. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\( f(0) = 20 \left( \frac{1}{4} \right)^0 \)[/tex].
4. Simplify the expression:
Note that any number raised to the power of 0 is 1. Thus, [tex]\( \left( \frac{1}{4} \right)^0 = 1 \)[/tex].
5. Calculate the result:
[tex]\( f(0) = 20 \times 1 = 20 \)[/tex].
Therefore, the initial value of the function [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex] when [tex]\( x = 0 \)[/tex] is 20.
So, on the graph, Chelsea would plot the point corresponding to [tex]\( (0, 20) \)[/tex]. This is her first step in graphing the function.
