Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \times 3^x \)[/tex], follow these steps:
1. Identify the function: The function given is [tex]\( f(x) = \frac{1}{9} \times 3^x \)[/tex].
2. Substitute the value: We need to find the value when [tex]\( x = 5 \)[/tex], so substitute 5 for [tex]\( x \)[/tex] in the function:
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
3. Calculate [tex]\( 3^5 \)[/tex]: First, compute [tex]\( 3^5 \)[/tex]:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = \frac{243}{9} = 27
\][/tex]
So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
Therefore, the correct answer is B. 27.
1. Identify the function: The function given is [tex]\( f(x) = \frac{1}{9} \times 3^x \)[/tex].
2. Substitute the value: We need to find the value when [tex]\( x = 5 \)[/tex], so substitute 5 for [tex]\( x \)[/tex] in the function:
[tex]\[
f(5) = \frac{1}{9} \times 3^5
\][/tex]
3. Calculate [tex]\( 3^5 \)[/tex]: First, compute [tex]\( 3^5 \)[/tex]:
[tex]\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
4. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, multiply the result by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = \frac{243}{9} = 27
\][/tex]
So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
Therefore, the correct answer is B. 27.
