Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \times 3^x \)[/tex], follow these steps:
1. Substitute 5 for [tex]\( x \)[/tex]: Start by replacing [tex]\( x \)[/tex] with 5 in the function. This gives us:
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
2. Calculate [tex]\( 3^5 \)[/tex]: The exponentiation of 3 to the power of 5 is:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Take the result from the previous step and multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = 27
\][/tex]
So, the value of [tex]\( f(5) \)[/tex] is 27. Therefore, the correct answer is:
C. 27
1. Substitute 5 for [tex]\( x \)[/tex]: Start by replacing [tex]\( x \)[/tex] with 5 in the function. This gives us:
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
2. Calculate [tex]\( 3^5 \)[/tex]: The exponentiation of 3 to the power of 5 is:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
3. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Take the result from the previous step and multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = 27
\][/tex]
So, the value of [tex]\( f(5) \)[/tex] is 27. Therefore, the correct answer is:
C. 27
