Answer
exponential;
$F(x)=\left(\frac{3}{2}\right)^x$
Work Step by Step
The ratio of consecutive values is constant $\left(\text{because } \dfrac{1}{\frac{2}{3}}=\dfrac{\frac{3}{2}}{1}=\dfrac{\frac{9}{4}}{\frac{3}{2}}=\dfrac{\frac{27}{8}}{\frac{9}{4}}=\dfrac{3}{2}\right)$, hence, the function is exponential with a growth factor of $\dfrac{3}{2}$.
The difference of consecutive values is not constant $\left(1-\frac{2}{3}\ne\frac{3}{2}-1\right)$), hence the function is not linear.
A function that models the data (with a growth factor of $\frac{3}{2}$ and $F(0)=1$) is $F(x)=\left(\frac{3}{2}\right)^x$.
