Exponential Decay
An exponential decay function is an exponential function where the
base, b, is in the interval 0 < b < 1. The graph of an exponential decay
function decreases when moving from left to right.
For example, the function
 is an exponential decay function
since the base,
 , is between 0 and 1.
From the graph, notice the following:
• The graph of the exponential decay function decreases when moving
from left to right.
• The graph intersects the y-axis at (0, 1).
• The domain is all real numbers.
• The range is all positive real numbers.
Let’s look at the relation between an exponential growth function and an
exponential decay function.
On the grid are the graphs of f(x) = 2x and
Notice that:
• The graph of
 is a reflection about the y-axis of the
graph y = 2x.
• Both graphs approach, but never quite reach, the x-axis.
Thus, we say that the x-axis is an asymptote of each graph.
This is why the range is (0, +∞) for both functions.
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