Question

question 15
evaluate the exponential function for the indicated value of x. round your answer to 2 decimal places, if necessary.
$f(x) = \frac{1}{4}(4)^{x + 3}$ for $f(1)$
$f(1) = \square$

Explanation:

Step1: Substitute x=1 into the function

Substitute \( x = 1 \) into \( f(x)=\frac{1}{4}(4)^{x + 3} \), we get \( f(1)=\frac{1}{4}(4)^{1+3} \).

Step2: Simplify the exponent

Calculate the exponent: \( 1 + 3=4 \), so the function becomes \( f(1)=\frac{1}{4}(4)^{4} \).

Step3: Calculate \( 4^4 \)

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

Step4: Multiply by \( \frac{1}{4} \)

Multiply \( 256 \) by \( \frac{1}{4} \): \( \frac{1}{4}\times256 = 64 \).

Answer:

\( 64.00 \)