Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(\frac12\right)^{x}$

• A. Exponential function, $f\left(4\right)=\frac{1}{16}$
• B. Exponential function, $f\left(4\right)=-16$
• C. Not an exponential function

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definition of an exponential function. An exponential function is of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (b > 0 and b ≠ 1), and 'x' is the exponent. In this case, the function is given as f(x) = (1/2)^x.
2. Step 2: Verify if the given function matches the form of an exponential function. Here, the base is b = 1/2, which is a positive number and not equal to 1. The exponent is 'x', which is a variable. Therefore, this is an exponential function.
3. Step 3: Identify the base and the power. The base of the function is b = 1/2, and the power is the variable x.
4. Step 4: Substitute x = 4 into the function to evaluate f(4). The function becomes f(4) = (1/2)^4. This means you need to raise 1/2 to the power of 4.
5. Step 5: Simplify the expression (1/2)^4. This involves multiplying 1/2 by itself four times: (1/2) * (1/2) * (1/2) * (1/2). Simplify this to find the value of f(4).