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=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=−7
.
The horizontal asymptote is at y equals negative 7 .
The horizontal asymptote is at y=0
.

Answer 1

In a typical exponential decay function, the graph approaches a horizontal asymptote as the x-values increase. The horizontal asymptote usually represents the value that the function approaches but never actually reaches.

Without seeing the specific graph, we can make some general observations based on common characteristics of exponential decay functions:

1. Behavior as x increases: The function will typically approach a certain value, which could be a positive number, zero, or a negative number depending on the specific function.

2. Common horizontal asymptotes: For exponential decay functions, the horizontal asymptote is often at \(y = 0\) if the function decays toward zero.

Given the provided options, the most common horizontal asymptote for an exponential decay function is \(y = 0\).

Therefore, the best response would be:

The horizontal asymptote is at y=0.