The exponential function represented by the table can be written in the form y=ab^x. find the values for a and b.

If this function can be written in the form y = ab^x, then we see that when x is inputted as 0, y is outputted as 4. This means that
                                          4 = ab^0
                                          a = 4
The value of a is 4.
We see that when x = 1, y = 2 thus
                                           y = 4b^x
                                          2 = 4(b^1)
                                          b = 1/2
The answers are a = 4 and b = 1/2