which graph represents an exponential decay function?

Explanation:

Step1: Recall exponential - decay property

An exponential - decay function has the form $y = a\cdot b^{x}$ where $a>0$ and $0 < b<1$. Its graph starts at a positive $y$ - intercept (when $x = 0$, $y=a$) and decreases as $x$ increases, approaching the $x$ - axis (horizontal asymptote $y = 0$) as $x\rightarrow+\infty$.

Step2: Analyze the given graphs

The first graph starts at a non - negative $y$ value (near $y=- 1$) for $x$ close to $0$ and decreases as $x$ increases, approaching the $x$ - axis. This is consistent with the behavior of an exponential decay function. The second graph increases rapidly as $x$ increases, which is the behavior of an exponential growth function.

Answer:

The first graph (the one that starts at a non - positive $y$ value for $x$ close to $0$ and decreases as $x$ increases, approaching the $x$ - axis) represents an exponential decay function.