Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \cdot 3^x \)[/tex], follow these steps:
1. Start with the given function:
[tex]\[
f(x) = \frac{1}{9} \cdot 3^x
\][/tex]
2. Substitute [tex]\( x \)[/tex] with 5:
[tex]\[
f(5) = \frac{1}{9} \cdot 3^5
\][/tex]
3. Calculate [tex]\( 3^5 \)[/tex]:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
4. Substitute [tex]\( 3^5 \)[/tex] back into the function:
[tex]\[
f(5) = \frac{1}{9} \cdot 243
\][/tex]
5. Simplify the multiplication:
[tex]\[
f(5) = \frac{243}{9}
\][/tex]
6. Perform the division:
[tex]\[
\frac{243}{9} = 27
\][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
So, the correct answer is:
C. 27
1. Start with the given function:
[tex]\[
f(x) = \frac{1}{9} \cdot 3^x
\][/tex]
2. Substitute [tex]\( x \)[/tex] with 5:
[tex]\[
f(5) = \frac{1}{9} \cdot 3^5
\][/tex]
3. Calculate [tex]\( 3^5 \)[/tex]:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
4. Substitute [tex]\( 3^5 \)[/tex] back into the function:
[tex]\[
f(5) = \frac{1}{9} \cdot 243
\][/tex]
5. Simplify the multiplication:
[tex]\[
f(5) = \frac{243}{9}
\][/tex]
6. Perform the division:
[tex]\[
\frac{243}{9} = 27
\][/tex]
Thus, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
So, the correct answer is:
C. 27
