Answer :
To find [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex], follow these steps:
1. Identify the function: We are given the function [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex]: We need to find [tex]\( f(5) \)[/tex], which means we substitute [tex]\( x = 5 \)[/tex] into the function.
3. Evaluate the expression:
- 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, multiply the result by [tex]\(\frac{1}{9}\)[/tex].
- [tex]\(\frac{1}{9} \times 243 = 27\)[/tex].
Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
So the correct answer is B. 27.
1. Identify the function: We are given the function [tex]\( f(x) = \frac{1}{9}(3)^x \)[/tex].
2. Substitute the value of [tex]\( x \)[/tex]: We need to find [tex]\( f(5) \)[/tex], which means we substitute [tex]\( x = 5 \)[/tex] into the function.
3. Evaluate the expression:
- 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, multiply the result by [tex]\(\frac{1}{9}\)[/tex].
- [tex]\(\frac{1}{9} \times 243 = 27\)[/tex].
Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\( 27 \)[/tex].
So the correct answer is B. 27.
