Let's solve the given function step by step to find the value of [tex]\( F(4) \)[/tex].
The function given is:
[tex]\[ F(x) = 5 \cdot \left(\frac{1}{2}\right)^x \][/tex]
We need to find [tex]\( F(4) \)[/tex], so we substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ F(4) = 5 \cdot \left(\frac{1}{2}\right)^4 \][/tex]
Firstly, calculate [tex]\(\left(\frac{1}{2}\right)^4\)[/tex]:
[tex]\[
\left(\frac{1}{2}\right)^4 = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{16}
\][/tex]
Next, multiply this result by 5:
[tex]\[
5 \cdot \frac{1}{16} = \frac{5}{16}
\][/tex]
Thus, [tex]\( F(4) = \frac{5}{16} \)[/tex].
Now, let's compare this with the given options:
A. [tex]\(\frac{5}{8}\)[/tex]
B. [tex]\(\frac{5}{2}\)[/tex]
C. [tex]\(\frac{5}{4}\)[/tex]
D. [tex]\(\frac{5}{16}\)[/tex]
The correct answer is:
D. [tex]\(\frac{5}{16}\)[/tex]
