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

1. Has a $y$-intercept of $(0, 2)$ and passes through the point $(3, 128)$.

   Hint (a):

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

   More help (a):

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

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

   Hint (b):

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

   Step (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.

   Answer (b):

   $y = 4 \cdot \left(\frac{1}{2}\right)^{x}$