Exponential and Logarithmic Functions: Exponential Growth and Decay

Graphing Exponential Growth and Decay

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You can recognize if a function represents an exponential growth or decay by looking at the b value of f(x) = bx. If b < 1 then the function represents an exponential decay. If b > 1, the function represents an exponential growth.

For example, the function f(x) = 3.5x represents an exponential growth. The function f(x) = (0.5)x represents an exponential decay.

The following is the graph of f(x) = 3.5x.

Graph of f of x is equal to three point five to the x power

This graph represents an exponential growth. Notice the graph increases from left to right at an exponential rate.

The following is the graph of f(x) = (0.5)x which can also be written as f(x) = one-half to the x power.

Graph of f of x is equal to one half to the x power

This graph represents an exponential decay. Notice the graph decreases from left to right at an exponential rate.

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