Question

without graphing, determine whether the function represents exponential growth or exponential decay. then find the y-intercept.
$f(x)=4(3)^x$
choose the correct answer below.
the function represents exponential decay.
the function represents exponential growth.

Explanation:

Step1: Identify growth/decay factor

An exponential function has the form $f(x)=a(b)^x$, where $b$ is the base. If $b>1$, it is growth; if $01$.

Step2: Find y-intercept

The y-intercept occurs at $x=0$. Substitute $x=0$ into the function:
$f(0)=4(3)^0=4(1)=4$

Answer:

The function represents exponential growth.
The y-intercept is $(0, 4)$