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Use the function below to find [tex]\( F(3) \)[/tex].

[tex]\[ F(x) = 4 \cdot \left(\frac{1}{3}\right)^x \][/tex]

A. [tex]\(\frac{4}{27}\)[/tex]

B. [tex]\(\frac{4}{81}\)[/tex]

C. [tex]\(\frac{4}{3}\)[/tex]

D. [tex]\(\frac{4}{9}\)[/tex]

Sagot :

GinnyAnswer
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]
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