The given function represents an exponential model if every consecutive value is the previus value multiplied by a costant b that is called the growth (decay) factor. We not then that this table represents an exponential model, because the decay factors is 2.

The recursive rule is f(0)=a and f(n)=b*f(n-1) with a the initial value (at n=0) and b is the growth factor (or decay factor if b<0).

Since a=0.75 and b=2 we then obtain the recursive rule: f(0)=0.75

\(f(n)=1/2*f(n-1)\)