Question

Question

Use the image to answer the 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
.
The horizontal asymptote is at y equals 0 .

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

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

The horizontal asymptote is at y=−7
.
The horizontal asymptote is at y equals negative 7 .
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Answer 1

The horizontal asymptote of an exponential decay function is usually located at \( y = 0 \), since as the value of \( x \) approaches infinity, the output of the function approaches but never actually reaches zero.

Without seeing the specific graph, if the solid curve corresponds to an exponential decay function, it typically approaches \( y = 0 \) as \( x \) increases.

Therefore, the correct response would likely be:

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