Use the image to answer the question.

Question

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

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

The horizontal asymptote is at y=0
𝑦
=
0
.
The horizontal asymptote is at y equals 0 .

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

Answer 1

The horizontal asymptote of an exponential decay function typically indicates the value that the function approaches as the input (usually represented as \( x \)) approaches infinity.

In many exponential decay functions of the form \( y = ae^{-bx} + c \), where \( a \) is a coefficient, \( b \) is a decay constant, and \( c \) is a constant added to the function (which shifts the graph vertically), the horizontal asymptote is determined by the value of \( c \).

Without the actual graph to visualize, the most common horizontal asymptote for exponential decay functions, particularly when they do not shift vertically, is \( y = 0 \).

Hence, if the function approaches zero as \( x \) goes to infinity, we conclude that the horizontal asymptote is at \( y = 0 \).

Therefore, among the provided responses, the most appropriate answer is:

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