Question

use the function below to find ( f(4) ).
( f(x) = \frac{1}{3} cdot 4^x )
a. ( \frac{64}{3} )
b. ( \frac{16}{3} )
c. ( \frac{256}{3} )
d. ( \frac{8}{3} )

Explanation:

Step1: Substitute x = 4 into the function

We have the function \( f(x)=\frac{1}{3}\cdot4^{x} \). To find \( f(4) \), we substitute \( x = 4 \) into the function. So we get \( f(4)=\frac{1}{3}\cdot4^{4} \).

Step2: Calculate \( 4^{4} \)

We know that \( 4^{4}=4\times4\times4\times4 = 256 \).

Step3: Multiply by \( \frac{1}{3} \)

Now we multiply 256 by \( \frac{1}{3} \), so \( f(4)=\frac{1}{3}\times256=\frac{256}{3} \).

Answer:

C. \( \frac{256}{3} \)