which function represents exponential growth?\no (f(x)=3x)\no (f(x)=x^{3})\no (f(x)=x + 3)\no (f(x)=3^{x})

Explanation:

Step1: Recall exponential - growth function form

The general form of an exponential - growth function is $f(x)=a\cdot b^{x}$, where $a> 0$ and $b > 1$.

Step2: Analyze each option

• For $f(x)=3x$, this is a linear function of the form $y = mx + c$ (here $m = 3$ and $c = 0$).
• For $f(x)=x^{3}$, this is a power function.
• For $f(x)=x + 3$, this is a linear function of the form $y=mx + c$ (here $m = 1$ and $c = 3$).
• For $f(x)=3^{x}$, it is in the form $y = a\cdot b^{x}$ with $a = 1$ and $b=3>1$, which represents exponential growth.

Answer:

$f(x)=3^{x}$