which graph represents an exponential growth function?

Explanation:

Step1: Recall exponential - growth property

An exponential growth function has the form $y = a\cdot b^x$ where $a>0$ and $b > 1$. Its graph starts from a positive $y$ - intercept (when $x = 0$, $y=a$) and increases rapidly as $x$ increases.

Step2: Analyze each graph

The first graph has a horizontal asymptote and increases slowly, not characteristic of exponential growth. The second graph is a linear - like graph. The third graph is a decay graph (decreases as $x$ increases). The fourth graph starts from a positive $y$ - value and increases rapidly as $x$ increases, which is the characteristic of an exponential growth function.

Answer:

The fourth graph represents an exponential growth function.