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 Atte

3 answers

Based on the description provided, the horizontal asymptote of an exponential decay function typically corresponds to the value that the function approaches as \( x \) goes to infinity. In many cases of exponential decay, this horizontal asymptote is a constant value that the function does not cross.

Since you mentioned that the solid curve intersects a marked point on the y-axis and assuming that this point is not at 0, the horizontal asymptote would often be at \( y = 0 \) unless stated otherwise.

If the graph of the exponential decay function approaches any other constant value as \( x \) increases, that would be the location of the horizontal asymptote.

Thus, the horizontal asymptote is likely to be at:

y = 0 (if no other specific point is given).

If additional information about the intersection point or specific values on the graph is available, that could define the asymptote differently. Please verify the graph for such indications.

Question
Using the discussed properties of exponential decay graphs, find the y-intercept of the function y=30(0.85)x
that models an exponential sequence.(1 point)
The y-intercept is at the point (0,
).

To find the y-intercept of the function \( y = 30(0.85)^x \), we need to evaluate the function at \( x = 0 \).

Substituting \( x = 0 \) into the equation:

\[ y = 30(0.85)^0 \]

Since any non-zero number raised to the power of 0 is 1, we have:

\[ y = 30(1) = 30 \]

Thus, the y-intercept is at the point:

\[ (0, 30) \]

So the answer is:

The y-intercept is at the point (0, 30).