Use the image to answer the question.

Question

A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 10 to 10, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a marked point on the y-axis.

Use the graph of the exponential decay function that models an exponential decay sequence to discuss the properties and determine the equation for the horizontal asymptote of the graph.

(1 point)
Responses

The horizontal asymptote is at y=−7
.
The horizontal asymptote is at y equals negative 7 .

The horizontal asymptote is at y=5
.
The horizontal asymptote is at y equals 5 .

The horizontal asymptote is at y=0.3
.
The horizontal asymptote is at y equals 0.3 .

The horizontal asymptote is at y=0
.

Answer 1

The horizontal asymptote of an exponential decay function typically occurs at the value that the function approaches as the input (x) goes to infinity. In the context of exponential decay, this is often a constant value that the function will never actually reach.

Based on the descriptions given about the graph—assuming it is an exponential decay function and there are no additional specific values indicated in the question regarding its actual positioning on the y-axis—the most standard form of a horizontal asymptote for an exponential decay function is at y = 0, as the function approaches zero but never actually touches it.

Thus, the correct response would be:

The horizontal asymptote is at y = 0.