Write an equation for an exponential function of the form $y=a·b^x$ that passes through the points $(2,18)$ and $(4,162)$. The steps of the process are outlined below if you need them.  

1. Write a system of two equations by replacing $x$ and $y$ with the coordinates of the two given points.

   Step (a):

   $18=a·b^2$

2. Solve for $a$ in terms of $b$ in one equation. Substitute this value into the other equation to obtain one equation with a single variable, $b$.

   Step (b):

   $a=\frac{18}{b^2}$

3. Solve your equation from part (b) for $b$.  

4. Use the value of $b$ from part (c) to determine the value of $a$.

5. Write the final equation.