Answer
exponential;
$H(x)=$4^x$
Work Step by Step
The ratio of consecutive values is constant (because $\dfrac{1}{\frac{1}{4}}=\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=4$), hence, the function is exponential with a common ratio of $4$.
The difference of consecutive values is not constant ($4-1=3\ne16-4=12$) hence, the function is not linear.
A function that models the data: (with a common ratio of $4$ and $H(0)=1$) is $H(x)=4^x$.
