Question

Exponential Decay Quick Check
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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=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.
The horizontal asymptote is at y equals 0 .

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

In an exponential decay function, the horizontal asymptote typically represents a value that the function approaches but never actually reaches as the x-values increase (go to infinity).

In many exponential decay scenarios, this horizontal asymptote is at \( y = 0 \), since the values of the function decrease towards zero but do not become negative. Therefore, without the specifics of your graph, the most common answer would likely be:

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

If the function has a positive lower limit, such as \( y = -7 \) or another constant, that could be the horizontal asymptote, but from a standard perspective on exponential decay, \( y = 0 \) is the usual choice.