y= 3(.75)^x

Question

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.

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

Answer 1

For the exponential decay function \( y = 3(0.75)^x \), as \( x \) approaches infinity, the term \( (0.75)^x \) approaches 0. Therefore, the function approaches a value of \( y = 0 \) as \( x \) becomes very large.

The horizontal asymptote of the function is thus:

\[ y = 0 \]

So, the answer is:

The horizontal asymptote is at \( y = 0 \).