The table below gives input and output values for the function h(x) = a x . input output -2 .0625 -1 .25 0 1 1 4 2 what is the value of a 2?

h(2) = 16

The table values are consistent with the definition ...

... h(x) = 4^x

Then ...

... h(2) = 4^2 = 16

How do we know?

When x increases by 1 unit, h(x) increases by a factor of 4, so we know the base of the exponential term is 4. When x=0, h(0) = 1, so we know the multiplier of the exponential term is 1.