Question

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

 

Answer 1

Step 1 :

To determine whether the given function is linear, exponential, or neither, first compute the average rate of change of with respect to and then compute the ratio of the consecutive outputs.

If the average rate of change is constant, then the function is linear.

If the ratio of consecutive outputs is constant, then the function is exponential.

Average rate of change            Ratio of consecutive outputs

 

Comments

Contd.....

Observe the above table, for the given function, the average rate of change from to is , and from to is .

Since the average rate of change is not constant, the function is not a linear function.

Step 2 :

Observe the above table, for the given function, the ratio of consecutive outputs from to is , from to is , and from to is .

Since the ratio of consecutive outputs is not constant, the function is not an exponential function.

Hence the function is neither linear nor exponential.

Solution :

The function is neither linear nor exponential.