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:
â€¢ The graph of the exponential decay function decreases when moving
from left to right.
â€¢ The graph intersects the yaxis at (0, 1).
â€¢ The domain is all real numbers.
â€¢ The range is all positive real numbers.
Letâ€™s look at the relation between an exponential growth function and an
exponential decay function.
On the grid are the graphs of f(x) = 2^{x} and
Notice that:
â€¢ The graph of
is a reflection about the yaxis of the
graph y = 2^{x}.
â€¢ Both graphs approach, but never quite reach, the xaxis.
Thus, we say that the xaxis is an asymptote of each graph.
This is why the range is (0, +∞) for both functions.
