Answer :
We are given the function
[tex]$$
f(x)=\frac{1}{9}\cdot 3^x.
$$[/tex]
To find [tex]$f(5)$[/tex], substitute [tex]$x = 5$[/tex] into the function:
[tex]$$
f(5)=\frac{1}{9}\cdot 3^5.
$$[/tex]
Next, calculate [tex]$3^5$[/tex]. Since
[tex]$$
3^5 = 3\times 3\times 3\times 3\times 3 = 243,
$$[/tex]
we have
[tex]$$
f(5)=\frac{1}{9}\cdot 243.
$$[/tex]
Finally, compute the product:
[tex]$$
\frac{243}{9} = 27.
$$[/tex]
Thus, the value of [tex]$f(5)$[/tex] is [tex]$27$[/tex], which corresponds to option C.
[tex]$$
f(x)=\frac{1}{9}\cdot 3^x.
$$[/tex]
To find [tex]$f(5)$[/tex], substitute [tex]$x = 5$[/tex] into the function:
[tex]$$
f(5)=\frac{1}{9}\cdot 3^5.
$$[/tex]
Next, calculate [tex]$3^5$[/tex]. Since
[tex]$$
3^5 = 3\times 3\times 3\times 3\times 3 = 243,
$$[/tex]
we have
[tex]$$
f(5)=\frac{1}{9}\cdot 243.
$$[/tex]
Finally, compute the product:
[tex]$$
\frac{243}{9} = 27.
$$[/tex]
Thus, the value of [tex]$f(5)$[/tex] is [tex]$27$[/tex], which corresponds to option C.
