An exponential function passes through the points $\left(2, 36\right)$ and $\left(4, 81\right)$.  

1. Write the equation of an exponential function that passes through the two given points and has a horizontal asymptote of $y = 0$.

   Hint (a):

   Use the form $y = a·b^{x}$.
   Substitute the coordinates of the points for $x$ and $y$ to obtain two equations and solve for $a$ and $b$.

2. If the function you wrote in part (a) is shifted so that it has a horizontal asymptote of $y = 20$, and it now passes through the points $\left(2, 56\right)$ and $\left(4, 101\right)$, what will the equation of the new function be?

   Hint (b):

   Add a $+ 20$ to the function found in part (b).