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.
The graph of an exponential decay function has the following properties:
1. The graph starts at an initial value (often referred to as the "y-intercept" or "starting point") and decreases rapidly at first.
2. As x increases, the y-values decrease, but the rate of decrease slows down over time.
3. The graph approaches but never reaches a horizontal line called the "horizontal asymptote."
4. The equation for the horizontal asymptote is given by y = 0, which makes sense because an exponential decay function will never reach zero but gets arbitrarily close to it as x increases.
In other words, the graph of an exponential decay function will start high and decrease gradually over time, approaching but never reaching the x-axis (which represents y = 0). The equation for the horizontal asymptote is y = 0.