Exponential Decay Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 2 to 12 and its y-axis ranges from negative 2 to 6, both by 2-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 to determine the equation for the horizontal asymptote of the sequence that is modeled by the graph.

(1 point)
The horizontal asymptote is at y=
.
Remaining Attempts : 3
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Answer 1

The horizontal asymptote of an exponential decay function typically indicates where the function approaches as the x-values increase towards infinity. This value is usually found by examining the behavior of the function as \(x\) increases.

In most cases for exponential decay functions, the horizontal asymptote is a constant value, often represented by \(y = k\), where \(k\) is the value the function approaches. In many exponential decay graphs, this constant is often zero, implying that the function approaches the x-axis but never actually reaches it.

If the graph you are examining doesn't provide explicit coordinates for the horizontal asymptote, a common assumption in general exponential decay is:

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

You would fill in the answer as:

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