Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex], follow these steps:
1. Understand the function: The function given is [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex]. This means for any input [tex]\( x \)[/tex], you first calculate [tex]\( 3^x \)[/tex], then multiply the result by [tex]\(\frac{1}{9}\)[/tex].
2. Substitute the given value: We need to find [tex]\( f(5) \)[/tex]. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = \frac{1}{9}(3)^5
\][/tex]
3. Calculate [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, take the result of [tex]\( 3^5 \)[/tex] and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is 27.
The correct answer is B. 27.
1. Understand the function: The function given is [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex]. This means for any input [tex]\( x \)[/tex], you first calculate [tex]\( 3^x \)[/tex], then multiply the result by [tex]\(\frac{1}{9}\)[/tex].
2. Substitute the given value: We need to find [tex]\( f(5) \)[/tex]. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = \frac{1}{9}(3)^5
\][/tex]
3. Calculate [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, take the result of [tex]\( 3^5 \)[/tex] and multiply it by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
f(5) = \frac{1}{9} \times 243 = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is 27.
The correct answer is B. 27.
