Question

which graph represents an exponential decay function?

Explanation:

Step1: Recall exponential decay

An exponential decay function has the form \( y = ab^x \) where \( 0 < b < 1 \). Its graph should decrease as \( x \) increases and approach a horizontal asymptote (usually the x - axis or a constant line) as \( x\to\infty \), and increase as \( x\to-\infty \) (if \( a>0 \)) or decrease as \( x\to-\infty \) (if \( a < 0 \)), but the key for decay is the behavior as \( x \) increases.

Step2: Analyze the first graph

The first graph (the upper one) starts at the origin, and as \( x \) increases (moves to the right), the graph decreases and gets closer to the horizontal line (the x - axis or a line parallel to it). This is consistent with the behavior of an exponential decay function.

Step3: Analyze the second graph

The second graph (the lower one) as \( x \) increases (moves to the right), the graph is decreasing, but it seems to be more like a function with a vertical asymptote (maybe a rational function) rather than an exponential function. Also, the shape and the way it approaches the axes are different from the typical exponential decay graph. Exponential decay graphs have a smooth, continuous decrease with a horizontal asymptote, while this graph has a steeper, more "hyperbola - like" decrease near the y - axis.

Answer:

The upper graph (the first graph shown)