To find [tex]\( F(3) \)[/tex] using the function [tex]\( F(x) = 4 \cdot \left( \frac{1}{3} \right)^x \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( F(x) \)[/tex]:
[tex]\[
F(3) = 4 \cdot \left( \frac{1}{3} \right)^3
\][/tex]
2. Compute [tex]\( \left( \frac{1}{3} \right)^3 \)[/tex]:
[tex]\[
\left( \frac{1}{3} \right)^3 = \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{27}
\][/tex]
3. Multiply the result by 4:
[tex]\[
F(3) = 4 \cdot \frac{1}{27} = \frac{4}{27}
\][/tex]
Therefore, the value of [tex]\( F(3) \)[/tex] is [tex]\( \frac{4}{27} \)[/tex].
The correct answer is:
A. [tex]\(\frac{4}{27}\)[/tex]
