Answer
Exponential function and $H (x)=4^x$.
Work Step by Step
We can see that the ratio of consecutive vales is fixed or constant.
That is, $\dfrac{1}{1/4}=\dfrac{4}{1}=\dfrac{16}{4}=\dfrac{4}{1}$
Thus, the function is an exponential function with a common ratio of $4$.
The difference of consecutive vales is not fixed or constant.
That is, $4-1=3 \ne 16-4=12$
Thus, the function is not a linear function.
So, we conclude that the function with common ratio $4$ and $H(0)=1$ has the model: $H (x)=Ca^x=1(4)^x=4^x$.
