IDENTIFY EXPONENTIAL BEHAVIOR

It is sometimes useful to know, if a set of data is exponential. One way to tell is to observe the shape of the graph. Another way is to observe the pattern in the set of data. 

Example 1 :

Determine whether the graph shown below displays exponential behavior.

Solution : 

The graph shows rapidly increasing values of y as x increases. This is characteristic of exponential behavior.

Example 2 :

Determine whether the graph shown below displays exponential behavior.

Solution : 

The graph shows rapidly decreasing values of y as x increases. This is characteristic of exponential behavior.

Example 3 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 10. Let’s see if there is a common factor among the range values

Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. 

Exponential function for the above data is

f(x)  =  (1/2)^x

Example 4 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 10. The range values have a common difference 6.

The data do not display exponential behavior, but rather linear behavior.

Example 5 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 1. Let’s see if there is a common factor among the range values

Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. 

Exponential function for the above data is

f(x)  =  6^x

Example 6 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 2. The range values have a common difference 4.

The data do not display exponential behavior, but rather linear behavior.

Example 7 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 1. The range values have a common difference 3.

The data do not display exponential behavior, but rather linear behavior.

Example 8 :

Determine whether the data set shown below displays exponential behavior.

Solution :

The domain values are at regular intervals of 1. Let’s see if there is a common factor among the range values

Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. 

Exponential function for the above data is

f(x)  =  1/2^x

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