Question

evaluate the function for the given value.

(y = \frac{1}{2} \cdot 4^x) for (x = 1)

(y = ?)

Explanation:

Identify the given function and value

We are given the exponential function:

$$ y = \frac{1}{2} \cdot 4^x $$

We need to evaluate this function at the specific value:

$$ x = 1 $$

Substitute the value into the function

Substitute \( x = 1 \) into the equation:

$$ y = \frac{1}{2} \cdot 4^1 $$

Simplify the exponent

Any number raised to the power of 1 is equal to itself:

$$ 4^1 = 4 $$

So the equation becomes:

$$ y = \frac{1}{2} \cdot 4 $$

Calculate the final product

Multiply the fraction by the integer:

$$ y = \frac{4}{2} = 2 $$

Answer:

Evaluate the function for the given value.
\( y = \frac{1}{2} \cdot 4^x \) for \( x = 1 \)
\( y = \) <blank>2</blank>