In Exercises 1924 the values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are. [HINT: See Example 1.]

–2  –1  0  1  2 

0.5  1.5  4.5  13.5  40.5 

8  4  2  1 

Which function in table is exponential, if there any exponential function then define its model also, table is shown below:
0  1  2  
0.5  1.5  4.5  13.5  40.5  
8  4  2  1 
Given information:
The provided table is:
0  1  2  
0.5  1.5  4.5  13.5  40.5  
8  4  2  1 
Consider the following data table,
0  1  2  
0.5  1.5  4.5  13.5  40.5  
8  4  2  1 
From the data table it can be observed that for every time value of x increases by 1, the value of
. This suggest that
Use the formula of exponential function,
Substitute
Substitute
in
Substitute
Substitute
in
Divide both side by
Thus, the exponential equation is
From the data table it can also be observed that for every time value of x increases by 1, the value of
. This suggest that
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