Question

evaluate the function for the given value.

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

(y = ?)

Explanation:

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<reasoning>

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:
\[ y = \frac{4}{2} = 2 \]
</reasoning>

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

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"Mathematics",
"Algebra",
"Exponential Function Evaluation"
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Answer:

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<reasoning>

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:
\[ y = \frac{4}{2} = 2 \]
</reasoning>

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

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