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=5 . The horizontal asymptote is at y equals 5 . The horizontal asymptote is at y=−7 .
Answers
GPT-4o mini
For an exponential decay function, the general form of the equation is typically given by:
\[ y = a e^{-bx} + c \]
where:
- \( a \) is a coefficient that affects the initial value,
- \( b \) is a positive constant that affects the rate of decay,
- \( c \) is the vertical shift of the graph.
The horizontal asymptote of an exponential decay function is determined by the value of \( c \). As \( x \) approaches infinity, the term \( e^{-bx} \) approaches 0, and thus the value of \( y \) approaches \( c \).
From the options provided, the horizontal asymptote can be:
- at \( y = 0.3 \)
- at \( y = 0 \)
- at \( y = 5 \)
- at \( y = -7 \)
To determine the correct answer, you would need the specific equation of the exponential decay function or some additional information derived from the graph. However, in standard cases, if no vertical shift (\( c \)) is indicated, the horizontal asymptote for a typical exponential decay function is \( y = 0 \).
Assuming no additional information contradicts that, we conclude that:
The horizontal asymptote is at \( y = 0 \).
\[ y = a e^{-bx} + c \]
where:
- \( a \) is a coefficient that affects the initial value,
- \( b \) is a positive constant that affects the rate of decay,
- \( c \) is the vertical shift of the graph.
The horizontal asymptote of an exponential decay function is determined by the value of \( c \). As \( x \) approaches infinity, the term \( e^{-bx} \) approaches 0, and thus the value of \( y \) approaches \( c \).
From the options provided, the horizontal asymptote can be:
- at \( y = 0.3 \)
- at \( y = 0 \)
- at \( y = 5 \)
- at \( y = -7 \)
To determine the correct answer, you would need the specific equation of the exponential decay function or some additional information derived from the graph. However, in standard cases, if no vertical shift (\( c \)) is indicated, the horizontal asymptote for a typical exponential decay function is \( y = 0 \).
Assuming no additional information contradicts that, we conclude that:
The horizontal asymptote is at \( y = 0 \).