Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$ .
$f\(\left\)(x\(\right\))=3\(\left\)(1.5\(\right\))^{x}$

• A. Exponential function, $f\(\left\)(4\(\right\))=410.06$
• B. Exponential function, $f\(\left\)(4\(\right\))=15.19$
• C. Not an exponential function

Answer: (B)

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 (the initial value), 'b' is the base (a positive constant), and 'x' is the exponent (a variable).
2. Step 2: Analyze the given function f(x) = 3(1.5)^x. Here, the constant 'a' is 3, the base 'b' is 1.5, and the exponent is the variable 'x'. This matches the form of an exponential function.
3. Step 3: Identify the base and the power. In this case, the base is 1.5, and the power is the variable 'x'.
4. Step 4: To evaluate the function at x = 4, substitute x = 4 into the function: f(4) = 3(1.5)^4. This means you will calculate 1.5 raised to the power of 4 and then multiply the result by 3.
5. Step 5: Perform the calculation step-by-step: First, compute 1.5^4, then multiply the result by 3 to find f(4). This will give you the value of the function at x = 4.