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. Identify the general form of an exponential function, which is f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.
2. Compare the given function f(x) = 3(1.5)^x with the general form. Here, 'a' is 3 and 'b' is 1.5, indicating that it is indeed an exponential function.
3. To evaluate the function at x = 4, substitute 4 for x in the function: f(4) = 3(1.5)^4.
4. Calculate the power (1.5)^4. This involves multiplying 1.5 by itself four times.
5. Multiply the result of (1.5)^4 by 3 to find f(4). This will give you the value of the function at x = 4.