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.

Answer 1

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.