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
• D. Exponential function, $f\left(4\right)=18$

Answer: (B)

Verified step by step guidance

1. Identify the given function: \(f(x) = 3(1.5)^{x}\). This is written in the form \(f(x) = a \cdot b^{x}\), where \(a\) is a constant and \(b\) is the base of the exponential.
2. Determine if the function is exponential by checking if the variable \(x\) is in the exponent. Since \(x\) is the exponent of the base \$1.5$, this confirms it is an exponential function.
3. Identify the base and the coefficient (power and base): the base is \$1.5\( and the coefficient (or initial value) is \)3$.
4. To evaluate the function at \(x=4\), substitute \$4\( for \)x\( in the function: \)f(4) = 3(1.5)^{4}$.
5. Calculate the value of \$1.5^{4}\( first, then multiply the result by \)3\( to find \)f(4)$.