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, and 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 constant.

Since the ratio of consecutive outputs is constant, the function is an exponential function.

The function is an exponential function.

Equation of exponential function : .

In a exponential function the ratio of consecutive outputs is the growth factor .

is the value of the function when .

Here and .

Substitute and in .

Equation of exponential function is .

The function is an exponential function.

Equation of exponential function is .