Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9} \cdot 3^x \)[/tex], follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
Begin by substituting 5 into the function for [tex]\( x \)[/tex], so you calculate [tex]\( f(5) = \frac{1}{9} \cdot 3^5 \)[/tex].
2. Calculate [tex]\( 3^5 \)[/tex]:
To do this, multiply 3 by itself five times:
[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 step 2, which is 243, and multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\frac{1}{9} \times 243 = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is 27.
The correct answer is C. 27.
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
Begin by substituting 5 into the function for [tex]\( x \)[/tex], so you calculate [tex]\( f(5) = \frac{1}{9} \cdot 3^5 \)[/tex].
2. Calculate [tex]\( 3^5 \)[/tex]:
To do this, multiply 3 by itself five times:
[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 step 2, which is 243, and multiply by [tex]\(\frac{1}{9}\)[/tex]:
[tex]\[
\frac{1}{9} \times 243 = 27
\][/tex]
Therefore, the value of [tex]\( f(5) \)[/tex] is 27.
The correct answer is C. 27.
