Use the graph of the exponential decay function to determine the equation for the horizontal asymptote of the sequence that is modeled by the graph.

(0,3) y=3(.75)^x

(1 point)
The horizontal asymptote is at y=.

1 answer

The horizontal asymptote of an exponential decay function of the form \( y = a(b^x) \) (where \( 0 < b < 1 \)) is determined by its behavior as \( x \) approaches infinity. For the function you've provided:

\[ y = 3(0.75)^x \]

As \( x \) approaches infinity, the term \( (0.75)^x \) approaches 0. Therefore, the value of \( y \) will approach 0.

Thus, the horizontal asymptote is at \( y = 0 \).

So, the answer is:

The horizontal asymptote is at y = 0.