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

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

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 .
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Answer 1

In an exponential decay function, the horizontal asymptote generally represents the value that the function approaches as x approaches positive or negative infinity. For most exponential decay functions of the form \( y = ab^x + k \), where \( b < 1 \), the horizontal asymptote is typically the constant \( k \).

Since the curve intersects the y-axis and given common behavior of exponential decay functions, if we assume it approaches a horizontal asymptote, that value would usually be a non-negative number, most often around y = 0, unless specified otherwise by the graph.

Based on the options provided, and without being able to see the image, the most typical scenario for an exponential decay function would have the horizontal asymptote at \( y = 0 \).

Therefore, the correct response would be:

The horizontal asymptote is at y = 0.