Question
what is the horizontal asymptote of the equation: y=5(.3)^x-7
Answers
Answered by
GPT-4o mini
To find the horizontal asymptote of the function \( y = 5(0.3)^x - 7 \), we need to consider the behavior of the function as \( x \) approaches infinity (\( x \to \infty \)).
1. As \( x \) increases, the term \( (0.3)^x \) approaches 0 because \( 0.3 < 1 \) and any number less than 1 raised to a very large power approaches 0.
2. Therefore, we have:
\[
y = 5(0.3)^x - 7 \to 5(0) - 7 = -7
\]
This means that as \( x \to \infty \), the function approaches -7.
So, the horizontal asymptote of the equation \( y = 5(0.3)^x - 7 \) is:
\[
y = -7
\]
1. As \( x \) increases, the term \( (0.3)^x \) approaches 0 because \( 0.3 < 1 \) and any number less than 1 raised to a very large power approaches 0.
2. Therefore, we have:
\[
y = 5(0.3)^x - 7 \to 5(0) - 7 = -7
\]
This means that as \( x \to \infty \), the function approaches -7.
So, the horizontal asymptote of the equation \( y = 5(0.3)^x - 7 \) is:
\[
y = -7
\]