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 1/2.

The recursive rule is f(0)=a and \(\displaystyle{f{{\left({n}\right)}}}={b}\cdot{f{{\left({n}-{1}\right)}}}\) with a the initial value (at n=0) and b is the growth factor (or decay factor if b

Since a=92 and \(\displaystyle{b}=\frac{{1}}{{2}}\) we then obtain the recursive rule: f(0)=96

\(\displaystyle{f{{\left({n}\right)}}}=\frac{{1}}{{2}}\cdot{f{{\left({n}-{1}\right)}}}\)

The recursive rule is f(0)=a and \(\displaystyle{f{{\left({n}\right)}}}={b}\cdot{f{{\left({n}-{1}\right)}}}\) with a the initial value (at n=0) and b is the growth factor (or decay factor if b

Since a=92 and \(\displaystyle{b}=\frac{{1}}{{2}}\) we then obtain the recursive rule: f(0)=96

\(\displaystyle{f{{\left({n}\right)}}}=\frac{{1}}{{2}}\cdot{f{{\left({n}-{1}\right)}}}\)