Question

without graphing, determine whether the function represents exponential growth or exponential decay.
$f(x) = 4(3)^x$
choose the correct answer below.
the function represents exponential decay.
the function represents exponential growth.
the y-intercept is . (type an integer or a decimal.)

Explanation:

Step1: Identify exponential form

The standard exponential function is $f(x) = a(b)^x$, where $a>0$.

Step2: Analyze base $b$

For $f(x)=4(3)^x$, $b=3$. Since $b>1$, it is growth.

Step3: Find y-intercept

Set $x=0$: $f(0)=4(3)^0 = 4(1) = 4$.

Answer:

The function represents exponential growth.
The y-intercept is 4.