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

\                    \                                                                     \                    \                                                                          \                  \                                                                           \                  \                                                                      \                           \

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.

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.

The function is neither linear nor exponential.