Consider the work done by the gas for the given volume $V$ and pressure $P.$ Assume that the pressure is inversely proportional to the volume. $($See Example $6.)$

A quantity of gas with an initial volume of $4$ cubic feet and a pressure of $1100$ pounds per square foot expands to a volume of $7$ cubic feet.

Find $k,$ the constant of proportionality.

$k=$

Find the work done. $($Round your answer to two decimal places.$)$

$$ ft$-1$b