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 1(a):

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

   Hint 2(a):

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

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

   Hint 1(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 $b$.

   Hint 3(b):

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

   Answer (b):

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