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 not equal to 1), and 'x' is the exponent.
2. Step 2: Analyze the given function f(x) = 3(1.5)^x. Here, '3' is the constant multiplier (a), '1.5' is the base (b), and 'x' is the exponent. This matches the form of an exponential function.
3. Step 3: Identify the base and the power. In this case, the base is b = 1.5, and the power is x. This confirms that the function is indeed an exponential function.
4. Step 4: To evaluate the function at x = 4, substitute x = 4 into the function. This gives f(4) = 3(1.5)^4. Use the rules of exponents to calculate (1.5)^4 and then multiply the result by 3.
5. Step 5: Simplify the expression to find the value of f(4). This involves calculating (1.5)^4 and then multiplying by 3. The final result will confirm the value of f(4).