A power plant's electrostatic precipitator $($EP$)$ currently removes $95\%$ of the

particles in the waste gas. The new law requires the factory to remove $99\%$ of the

particles in the waste gas. The collection efficiency of the EP is given by

$=1-$exp$(-\frac{Aw}{Q})$ where $A$ is the area of the collection plate, $Q$ is the flow rate of

the gas stream, and $w$ is the effective particle drift velocity. The plant's original

EP collection plate area is $100m^2.$ If the plant were to install a new collection

plate, what must be the new plate's area to meet the new emission standard?

$(5$ marks$)$