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=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
.

Answer 1

In an exponential decay function, the graph approaches a horizontal line as x approaches positive or negative infinity. This line is referred to as the horizontal asymptote.

Typically, for a general exponential decay function of the form:

\[ y = a \cdot e^{-bx} + c \]

where \( a \) and \( b \) are constants, and \( c \) represents a vertical shift,

the horizontal asymptote will be located at \( y = c \).

If there is no vertical shift (i.e., \( c = 0\)), the horizontal asymptote will be at \( y = 0 \).

Given the response options you provided, without additional information about the specific parameters of the decay function (like the initial value or a vertical shift), we can determine the horizontal asymptote based on what is typical for exponential decay.

- If the function does not have a vertical shift, then the horizontal asymptote would be at **y = 0**.
- If there is a vertical shift defined by the decay function, that would determine the specific asymptote.

Assuming you're looking for the most common scenario without any other information indicating a shift, the answer would be:

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