The data given below provides the distance required for a particular type of car to stop when traveling at a variety of speeds. A reasonable model for braking distance is $d = as^k$, where $d$ is distance, $s$ is speed, and $a$ and $k$ are constants. Use the data in the table to find values for $a$ and $k$, and also type out the equation that models the breaking distance.

$$\begin{array}{c|c|c|c|c|} \mbox{Speed (MPH)} & 10 & 20 & 30 & 40 \\\hline \mbox{Distance (Feed)} & 20 & 80 & 180 & 320 \end{array}$$

$a =$
$k =$
Model: