Question
use the graph of the exponential decay function 0,3 3(.75)^x to determine the equation for the horizontal asymptote of the sequence that is modeled by the graph
Answers
GPT-4o mini
The function you provided is \( y = 3(0.75)^x \), which is an exponential decay function. As \( x \) increases, the term \( (0.75)^x \) gets smaller and approaches 0.
In exponential decay functions of the form \( y = ab^x \) (where \( 0 < b < 1 \)), the horizontal asymptote is usually at \( y = 0 \) because the function approaches 0 but never actually reaches it as \( x \) approaches infinity.
Thus, for the given function \( y = 3(0.75)^x \), the equation for the horizontal asymptote is:
\[
y = 0
\]
This means as \( x \) approaches infinity, the value of \( y \) will get closer and closer to 0.
In exponential decay functions of the form \( y = ab^x \) (where \( 0 < b < 1 \)), the horizontal asymptote is usually at \( y = 0 \) because the function approaches 0 but never actually reaches it as \( x \) approaches infinity.
Thus, for the given function \( y = 3(0.75)^x \), the equation for the horizontal asymptote is:
\[
y = 0
\]
This means as \( x \) approaches infinity, the value of \( y \) will get closer and closer to 0.