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Wednesday 29th of June
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 Depdendent Variable

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 Dependent Variable

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# 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 y-axis 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) = 2x and

Notice that:

â€¢ The graph of is a reflection about the y-axis of the graph y = 2x.

â€¢ 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.