Question

graph: $f(x) = \frac{3}{2}(2)^x$
step 1: calculate the initial value of the function.
$f(0) = $ dropdown with 0, 1, 1.5
graph of coordinate plane with x from -2 to 2 and y from 1 to 4
check button

Explanation:

Step1: Substitute \( x = 0 \) into the function

The function is \( f(x)=\frac{3}{2}(2)^x \). When \( x = 0 \), we use the property of exponents that \( a^0 = 1 \) (for \( a
eq0 \)). So substitute \( x = 0 \) into the function: \( f(0)=\frac{3}{2}(2)^0 \).

Step2: Evaluate the exponent and simplify

Since \( 2^0 = 1 \), then \( f(0)=\frac{3}{2}\times1=\frac{3}{2}=1.5 \).

Answer:

\( f(0) = 1.5 \)