Find a possible exponential function in $y = a · b^{x}$ form that represents each situation described below.

1. Has an initial value of $2$ and passes through the point $\left(3, 128\right)$.

   Hint (a):

   Since it has an initial value of $2$, the value of a is $2$.
   Substitute this into the general equation: $y = ab^{x}$

   More Help (a):

   Substitute the values $3$ and $128$ for $x$ and $y$, respectively, then solve for $b$.

2. Passes through the points $\left(0, 4\right)$ and $\left(2, 1\right)$.

   Hint (b):

   Create two equations substituting the values of the ordered pairs for x and y into the equation $y = ab^{x}$.

   Hint 2(b):

   Solve the system of equations for a and b.

   More Help (b):

   Be sure you use your results for a and b to write the equation.