Identify any asymptotes of the graph.
y = 1.08^5x
To identify the asymptotes of the graph of the function y = 1.08^5x, we need to consider the behavior of the function as x approaches positive infinity or negative infinity.
An asymptote is a line that the graph of a function approaches but does not intersect. In this case, we are looking for vertical asymptotes, which are vertical lines that the graph approaches.
To determine the asymptotes, we first need to understand the behavior of the function as x approaches positive infinity and negative infinity.
As x approaches positive infinity (x → +∞), the function y = 1.08^5x will grow exponentially since the base, 1.08, is greater than 1. Therefore, the graph will approach but never touch the y-axis (x = 0).
As x approaches negative infinity (x → -∞), the function y = 1.08^5x will shrink exponentially because raising a number greater than 1 to a negative power results in a fraction approaching zero. However, the function will never reach zero, so the graph will never intersect the y-axis.
Therefore, the vertical asymptote of the graph of y = 1.08^5x is the y-axis, which is represented by the equation x = 0.