Question

which graph represents exponential decay?

Explanation:

Step1: Recall exponential decay graph properties

Exponential decay functions have the form \( y = ab^x \) where \( 0 < b < 1 \). Their graphs are curves (not straight lines) that decrease as \( x \) increases, approaching the \( x \)-axis (horizontal asymptote) without crossing it, and increase as \( x \) decreases (for \( a>0 \)).

Step2: Analyze each graph

• Top - Left: The graph is increasing as \( x \) increases (exponential growth, since \( b > 1 \)).
• Top - Middle: This is a straight line (linear function), not exponential.
• Top - Right: The graph decreases as \( x \) increases, is a curve, and approaches the \( x \)-axis. It matches exponential decay.
• Bottom - Left: The graph increases as \( x \) increases (exponential growth in the right - hand direction, but the left - hand behavior also suggests growth - like, not decay).

Answer:

The graph on the Top - Right (the third graph in the top row)